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A straight line is a half-turn, so the correct sum is 180°."},{"text":"360°.","correct":false,"explanation":"360° is the angle sum around a point, representing a full turn. A straight line represents only a half-turn, so its angle sum is 180°."},{"text":"270°.","correct":false,"explanation":"270° represents three-quarters of a full turn and is not the straight-line angle sum. Angles on a straight line always add to 180°."}]},{"id":"c771ae88-202c-cfb0-c47b-d035fdcd0b25","cardType":"basic","points":1,"front":"Two straight lines cross. What is true about vertically opposite angles?","back":"They are equal.","mcqOptions":[{"text":"They are equal.","correct":true,"explanation":"Vertically opposite angles are formed directly across from one another when two straight lines intersect, and each pair always has the same size."},{"text":"They are adjacent.","correct":false,"explanation":"Adjacent angles lie next to each other and share a side, whereas vertically opposite angles lie across the intersection. Vertically opposite angles are equal."},{"text":"They are always unequal.","correct":false,"explanation":"The angles may look different because of the diagram’s orientation, but vertically opposite angles formed by intersecting straight lines are always equal."},{"text":"They are on the same side.","correct":false,"explanation":"Angles on the same side of an intersection are adjacent rather than vertically opposite. Vertically opposite angles lie across from each other and are equal."}]},{"id":"f1ef0067-3fe8-2609-ca59-3862f831c11f","cardType":"basic","points":1,"front":"What is the angle sum in a triangle?","back":"180°.","mcqOptions":[{"text":"180°.","correct":true,"explanation":"The three interior angles of every triangle add to 180°, regardless of the triangle’s side lengths or whether it is acute, right-angled or obtuse."},{"text":"90°.","correct":false,"explanation":"90° is the size of one right angle, not the total of a triangle’s interior angles. The three angles in a triangle add to 180°."},{"text":"360°.","correct":false,"explanation":"360° is the sum of angles around a point or in a quadrilateral. A triangle has three interior angles whose sum is 180°."},{"text":"270°.","correct":false,"explanation":"270° can result from confusing a triangle’s angle sum with three right angles. The interior angles of any triangle add to 180°."}]},{"id":"fd2548fd-0d3b-b621-19af-9ad760f18b34","cardType":"cloze","points":null,"front":"Angles on a [ ] add to [ ].","back":"Angles on a straight line add to 180°.","mcqOptions":[{"text":"Angles on a straight line add to 180°.","correct":true,"explanation":"A straight line represents a half-turn, which measures 180°. Therefore, all adjacent angles formed along the straight line must total 180°."},{"text":"Angles on a straight line add to 90°.","correct":false,"explanation":"90° is a right angle and represents only a quarter-turn. A straight line is a half-turn, so angles on it add to 180°."},{"text":"Angles on a right angle add to 180°.","correct":false,"explanation":"Angles dividing a right angle total 90°, not 180°. The 180° rule applies to angles on a straight line because it forms a half-turn."},{"text":"Angles on a full turn add to 90°.","correct":false,"explanation":"A full turn measures 360°, while 90° is only a quarter-turn. The required rule is that angles on a straight line add to 180°."}]},{"id":"2a680b02-05c7-a8a3-a022-f0cbaa9bd938","cardType":"basic","points":1,"front":"Two straight lines cross. One angle is 68°. What is the vertically opposite angle?","back":"68°.","mcqOptions":[{"text":"68°.","correct":true,"explanation":"Vertically opposite angles are always equal, so the angle directly opposite the given 68° angle also measures 68°."},{"text":"112°.","correct":false,"explanation":"112° is the adjacent angle because it combines with 68° to make 180°. The vertically opposite angle is equal to the original angle, so it is 68°."},{"text":"34°.","correct":false,"explanation":"Halving 68° is not part of the vertically opposite angle rule. Vertically opposite angles have equal measures, so the required angle is 68°."},{"text":"292°.","correct":false,"explanation":"Subtracting 68° from 360° finds the remainder of a full turn, not one vertically opposite angle. The opposite angle is equal to 68°."}]},{"id":"e9187710-5ec9-a1dc-440b-4f6397073507","cardType":"basic","points":1,"front":"An angle is 68° on a straight line. What is the adjacent angle?","back":"112°.","mcqOptions":[{"text":"112°.","correct":true,"explanation":"Adjacent angles on a straight line add to 180°. Subtracting gives 180° - 68° = 112°, so the adjacent angle is 112°."},{"text":"68°.","correct":false,"explanation":"68° would be the vertically opposite angle, not the adjacent one. Adjacent angles on a straight line total 180°, giving 180° - 68° = 112°."},{"text":"22°.","correct":false,"explanation":"Subtracting from 90° incorrectly treats the pair as complementary angles. Angles on a straight line total 180°, so the adjacent angle is 112°."},{"text":"292°.","correct":false,"explanation":"Subtracting from 360° incorrectly uses the full-turn rule. The two adjacent angles form a straight line, so the calculation is 180° - 68° = 112°."}]},{"id":"2dadf9ae-b90d-f935-ed0a-2b48f0d1827b","cardType":"cloze","points":null,"front":"The notation $AB \\parallel CD$ means line [ ].","back":"The notation $AB \\parallel CD$ means line AB is parallel to CD.","mcqOptions":[{"text":"AB is parallel to CD","correct":true,"explanation":"The symbol $\\parallel$ means “is parallel to”, so $AB \\parallel CD$ states that lines AB and CD remain the same distance apart and never meet."},{"text":"AB is perpendicular to CD","correct":false,"explanation":"Perpendicular lines meet at 90° and are represented by a different symbol. The symbol $\\parallel$ states that AB is parallel to CD."},{"text":"AB intersects CD at 45°","correct":false,"explanation":"The parallel symbol gives no 45° intersection; parallel lines do not intersect. The notation means that AB is parallel to CD."},{"text":"AB is equal in length to CD","correct":false,"explanation":"Matching lengths are shown with equality notation or matching tick marks, not the parallel symbol. $AB \\parallel CD$ means AB is parallel to CD."}]},{"id":"73f267ce-496c-c09e-3086-875b537d14eb","cardType":"basic","points":1,"front":"On a diagram, how are parallel lines often marked?","back":"With matching arrows.","mcqOptions":[{"text":"With matching arrows.","correct":true,"explanation":"Matching arrow markings placed on two or more lines show that those lines are parallel. Different arrow styles can distinguish separate sets of parallel lines."},{"text":"With matching ticks.","correct":false,"explanation":"Matching tick marks usually show that line segments have equal lengths, not that lines are parallel. Parallel lines are identified using matching arrow markings."},{"text":"With right-angle squares.","correct":false,"explanation":"A small square marks a 90° angle and therefore indicates perpendicular lines. Parallel lines are instead shown using matching arrow markings."},{"text":"With matching angle arcs.","correct":false,"explanation":"Matching arcs indicate that particular angles are equal, rather than directly marking lines as parallel. Parallel lines are conventionally identified by matching arrows."}]},{"id":"4858bc40-8818-c9c9-2d2e-1e21bbdee70e","cardType":"basic","points":1,"front":"Where is the interior region for two parallel lines?","back":"The space between the parallel lines.","mcqOptions":[{"text":"The space between the parallel lines.","correct":true,"explanation":"The interior region consists of all the space lying between the two parallel lines, regardless of the angle or position of the transversal."},{"text":"The space outside the parallel lines.","correct":false,"explanation":"The space outside the two lines is the exterior region. The interior region is the space between the parallel lines."},{"text":"The space above both parallel lines.","correct":false,"explanation":"The area above both lines is only part of the exterior region. The interior region is the complete space between the parallel lines."},{"text":"The space on the transversal line.","correct":false,"explanation":"The transversal crosses the parallel lines but does not define the interior region by itself. The interior region is the space between the parallel lines."}]},{"id":"7166ff1f-2069-b4c9-34eb-bf3585738fae","cardType":"basic","points":1,"front":"What angle rule is shown by an F-shape in parallel lines?","back":"Corresponding angles are equal.","mcqOptions":[{"text":"Corresponding angles are equal.","correct":true,"explanation":"An F-shape identifies angles in the same relative position at the two intersections. These are corresponding angles, and they are equal when the lines are parallel."},{"text":"Alternate angles are equal.","correct":false,"explanation":"Alternate angles are equal, but they are identified by a Z-shape rather than an F-shape. An F-shape shows that corresponding angles are equal."},{"text":"Vertically opposite angles are equal.","correct":false,"explanation":"Vertically opposite angles occur across from each other at a single intersection. An F-shape spans two intersections and shows that corresponding angles are equal."},{"text":"Co-interior angles add to 180°.","correct":false,"explanation":"Co-interior angles form a C-shape and sum to 180°. An F-shape instead identifies corresponding angles, which are equal when the lines are parallel."}]},{"id":"51337a03-2464-ebd9-bbb3-605a32b3677a","cardType":"cloze","points":null,"front":"Corresponding angles are in the [ ] at each crossing.","back":"Corresponding angles are in the same relative position at each crossing.","mcqOptions":[{"text":"same relative position","correct":true,"explanation":"At each intersection, corresponding angles occupy the same position relative to the transversal and the parallel line, such as above-right at both crossings."},{"text":"opposite relative position","correct":false,"explanation":"Angles in opposite positions at the two intersections are associated with alternate-angle arrangements. Corresponding angles occupy the same relative position at each crossing."},{"text":"same interior region","correct":false,"explanation":"Merely lying within the interior region does not make two angles corresponding. They must occupy the same relative position at their respective crossings."},{"text":"adjacent relative position","correct":false,"explanation":"Adjacent positions describe angles next to one another at an intersection, not corresponding angles. Corresponding angles occupy the same relative position at each crossing."}]},{"id":"5cf50004-a6d4-27ab-2547-2bc5ee34bf0c","cardType":"basic","points":1,"front":"In an F-shape, one corresponding angle is 58°. What is the other?","back":"58°.","mcqOptions":[{"text":"58°.","correct":true,"explanation":"Corresponding angles formed by a transversal crossing parallel lines are equal, so the angle corresponding to 58° also measures 58°."},{"text":"122°.","correct":false,"explanation":"Subtracting 58° from 180° finds a supplementary angle, not the corresponding angle. Corresponding angles are equal, so the other angle is 58°."},{"text":"29°.","correct":false,"explanation":"Halving 58° has no basis in the corresponding-angle rule. Corresponding angles in parallel lines are equal, so the other angle is 58°."},{"text":"116°.","correct":false,"explanation":"Doubling 58° does not find a corresponding angle. Corresponding angles formed by a transversal across parallel lines are equal, making the other angle 58°."}]},{"id":"28203d6b-bc70-0c96-9874-d1adcbd7896a","cardType":"basic","points":1,"front":"What angle rule is shown by a Z-shape in parallel lines?","back":"Alternate angles are equal.","mcqOptions":[{"text":"Alternate angles are equal.","correct":true,"explanation":"A Z-shape identifies alternate angles on opposite sides of the transversal. When the two lines are parallel, these alternate angles are equal."},{"text":"Corresponding angles are equal.","correct":false,"explanation":"Corresponding angles are equal, but they are recognised using an F-shape. A Z-shape identifies alternate angles, which are equal between parallel lines."},{"text":"Vertically opposite angles are equal.","correct":false,"explanation":"Vertically opposite angles lie across from each other at one intersection. A Z-shape uses two intersections and identifies alternate angles as equal."},{"text":"Co-interior angles add to 180°.","correct":false,"explanation":"Co-interior angles are identified by a C-shape and sum to 180°. A Z-shape instead shows alternate angles, which are equal."}]},{"id":"9af67a58-6f28-fa0a-35dd-9491d47b4f1a","cardType":"cloze","points":null,"front":"Alternate angles are on [ ] of the transversal.","back":"Alternate angles are on opposite sides of the transversal.","mcqOptions":[{"text":"opposite sides","correct":true,"explanation":"Alternate angles lie on opposite sides of the transversal at different intersections. With parallel lines, the pair of alternate angles has equal measures."},{"text":"the same side","correct":false,"explanation":"Interior angles on the same side of a transversal are co-interior and sum to 180°. Alternate angles lie on opposite sides of the transversal."},{"text":"parallel sides","correct":false,"explanation":"The lines themselves may be parallel, but this does not describe the angles’ positions relative to the transversal. Alternate angles lie on opposite sides of it."},{"text":"adjacent sides","correct":false,"explanation":"Adjacent angles share a vertex at one intersection, whereas alternate angles occur at different intersections. They lie on opposite sides of the transversal."}]},{"id":"6cf71cac-c661-1bd9-05c9-8ac82fd00f05","cardType":"basic","points":1,"front":"In a Z-shape, one alternate angle is 34°. What is the other?","back":"34°.","mcqOptions":[{"text":"34°.","correct":true,"explanation":"Alternate angles formed when a transversal crosses parallel lines are equal, so the angle alternate to 34° also measures 34°."},{"text":"146°.","correct":false,"explanation":"Subtracting 34° from 180° gives a supplementary angle, not the alternate angle. Alternate angles between parallel lines are equal, so the answer is 34°."},{"text":"68°.","correct":false,"explanation":"Doubling 34° is not part of the alternate-angle rule. Alternate angles formed across parallel lines are equal, so the other angle is 34°."},{"text":"17°.","correct":false,"explanation":"Halving 34° does not determine an alternate angle. Alternate angles between parallel lines have equal measures, so the other angle is 34°."}]},{"id":"0eeaf13c-cfdf-226d-cbcc-96f2b5ce8a73","cardType":"basic","points":1,"front":"What angle rule is shown by a C-shape in parallel lines?","back":"Co-interior angles add to 180°.","mcqOptions":[{"text":"Co-interior angles add to 180°.","correct":true,"explanation":"A C-shape identifies co-interior angles lying between the parallel lines on the same side of the transversal. These angles are supplementary, so they total 180°."},{"text":"Corresponding angles are equal.","correct":false,"explanation":"Corresponding angles are equal but are identified by an F-shape. A C-shape identifies co-interior angles, whose measures add to 180°."},{"text":"Alternate angles are equal.","correct":false,"explanation":"Alternate angles are equal but form a Z-shape across the transversal. A C-shape identifies co-interior angles, which add to 180°."},{"text":"Co-interior angles add to 90°.","correct":false,"explanation":"Confusing supplementary angles with complementary angles produces 90°. Co-interior angles between parallel lines are supplementary, so their measures add to 180°."}]},{"id":"94603cc7-ac27-f366-f425-a97f09c6f9b7","cardType":"cloze","points":null,"front":"Co-interior angles are inside the parallel lines and on the [ ] of the transversal.","back":"Co-interior angles are inside the parallel lines and on the same side of the transversal.","mcqOptions":[{"text":"same side","correct":true,"explanation":"Co-interior angles lie between the parallel lines on the same side of the transversal. When the lines are parallel, these angles have a total of 180°."},{"text":"opposite side","correct":false,"explanation":"Angles inside the parallel lines on opposite sides of the transversal are alternate angles, not co-interior angles. Co-interior angles are on the same side and sum to 180°."},{"text":"alternating sides","correct":false,"explanation":"Alternating sides describes the arrangement of alternate angles. Co-interior angles instead lie inside the parallel lines on the same side of the transversal."},{"text":"perpendicular side","correct":false,"explanation":"A transversal crosses the parallel lines rather than defining a perpendicular side. Co-interior angles are identified by being inside the lines on the same side of the transversal."}]},{"id":"014721e5-46e8-7d2b-bc72-93f00d1987e7","cardType":"basic","points":1,"front":"One co-interior angle is 118°. What is the other?","back":"62°.","mcqOptions":[{"text":"62°.","correct":true,"explanation":"Co-interior angles between parallel lines sum to 180°. Subtracting gives $180°-118°=62°$, so the other angle is 62°."},{"text":"118°.","correct":false,"explanation":"This treats the co-interior angles as equal. They are supplementary, so the required calculation is $180°-118°=62°$."},{"text":"242°.","correct":false,"explanation":"This results from incorrectly subtracting 118 from 360. Co-interior angles sum to 180°, so the other angle is $180°-118°=62°$."},{"text":"59°.","correct":false,"explanation":"This value comes from halving 118°, but co-interior angles are not found by halving. Their sum is 180°, giving $180°-118°=62°$."}]},{"id":"20f21cba-8c80-8389-96dd-9a0744384f7c","cardType":"basic","points":1,"front":"In an isosceles triangle, which angles are equal?","back":"The angles opposite the equal sides.","mcqOptions":[{"text":"The angles opposite the equal sides.","correct":true,"explanation":"In an isosceles triangle, equal sides have equal opposite angles. Therefore, the two angles opposite the equal sides are equal."},{"text":"The vertex angle and one base angle.","correct":false,"explanation":"The vertex angle and a base angle are not generally equal; they become equal only in an equilateral triangle. The equal angles lie opposite the equal sides."},{"text":"The angles opposite the unequal sides.","correct":false,"explanation":"An isosceles triangle normally has only one unequal side, so this does not identify the equal angles. The equal angles are opposite the two equal sides."},{"text":"The angles touching the same equal side.","correct":false,"explanation":"The angles touching a particular equal side are the vertex angle and one base angle, which need not match. Equal angles are opposite the equal sides."}]},{"id":"5d8b3029-e8e9-e616-ac4e-63a069bb070f","cardType":"cloze","points":null,"front":"A parallelogram has both pairs of [ ].","back":"A parallelogram has both pairs of opposite sides parallel.","mcqOptions":[{"text":"opposite sides parallel","correct":true,"explanation":"A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. Its opposite sides are also equal in length."},{"text":"adjacent sides parallel","correct":false,"explanation":"Adjacent sides meet at a vertex, so they cannot be parallel. A parallelogram is defined by having both pairs of opposite sides parallel."},{"text":"opposite sides perpendicular","correct":false,"explanation":"Opposite sides of a parallelogram run in the same direction and are parallel, not perpendicular. Perpendicular sides meet at an angle of 90°."},{"text":"adjacent sides perpendicular","correct":false,"explanation":"Adjacent sides of a parallelogram meet but are not necessarily perpendicular; only rectangles and squares have four right angles. Both pairs of opposite sides are parallel."}]},{"id":"0a177254-87f9-47db-95a2-d89886da48d5","cardType":"basic","points":1,"front":"In parallelogram $ABCD$, which side is parallel to $CD$?","back":"$AB$.","mcqOptions":[{"text":"$AB$.","correct":true,"explanation":"In parallelogram $ABCD$, the vertices are named consecutively. This makes $AB$ opposite $CD$, and opposite sides of a parallelogram are parallel."},{"text":"$BC$.","correct":false,"explanation":"Side $BC$ meets $CD$ at vertex $C$, so the sides are adjacent rather than parallel. The opposite side parallel to $CD$ is $AB$."},{"text":"$AD$.","correct":false,"explanation":"Side $AD$ meets $CD$ at vertex $D$, so these are adjacent sides. The side opposite and parallel to $CD$ is $AB$."},{"text":"$AC$.","correct":false,"explanation":"The line $AC$ is a diagonal joining opposite vertices, not a side of the parallelogram. The side parallel to $CD$ is $AB$."}]},{"id":"e1d6af26-0f7e-aba7-5622-7a24e21c8a5c","cardType":"basic","points":1,"front":"In parallelogram $ABCD$, which side is parallel to $BC$?","back":"$AD$.","mcqOptions":[{"text":"$AD$.","correct":true,"explanation":"In parallelogram $ABCD$, side $AD$ is opposite side $BC$. Opposite sides of every parallelogram are parallel, so $AD$ is parallel to $BC$."},{"text":"$AB$.","correct":false,"explanation":"Side $AB$ meets $BC$ at vertex $B$, making them adjacent rather than parallel. The opposite side parallel to $BC$ is $AD$."},{"text":"$CD$.","correct":false,"explanation":"Side $CD$ meets $BC$ at vertex $C$, so these sides are adjacent. The side opposite and parallel to $BC$ is $AD$."},{"text":"$BD$.","correct":false,"explanation":"The line $BD$ is a diagonal rather than a side, and it is not generally parallel to $BC$. The required opposite side is $AD$."}]},{"id":"4f5f7025-c292-4e27-fa29-b2be8b2c3245","cardType":"basic","points":1,"front":"What is a diagonal in a parallelogram?","back":"A line joining opposite corners.","mcqOptions":[{"text":"A line joining opposite corners.","correct":true,"explanation":"A diagonal connects two non-adjacent, opposite vertices of a polygon. A parallelogram has two diagonals, each joining one pair of opposite corners."},{"text":"A line joining adjacent corners.","correct":false,"explanation":"A line joining adjacent corners forms one of the parallelogram’s sides, not a diagonal. A diagonal joins two opposite corners."},{"text":"A line joining opposite side midpoints.","correct":false,"explanation":"Joining the midpoints of opposite sides creates a line through the parallelogram but not a diagonal. A diagonal connects opposite corners."},{"text":"A line joining the centre to a corner.","correct":false,"explanation":"A segment from the centre to a corner is only half of a diagonal. A complete diagonal joins one corner to the opposite corner."}]},{"id":"5d5fad54-4b21-5d8d-d055-af2d53c6acf2","cardType":"basic","points":1,"front":"Isosceles triangle $EFG$ has $EG=FG$ and $\\angle GEF=68°$. What is $\\angle EFG$?","back":"68°.","mcqOptions":[{"text":"68°.","correct":true,"explanation":"Sides $EG$ and $FG$ are equal, so their opposite angles at $F$ and $E$ are equal. Therefore, $angle EFG=angle GEF=68°$."},{"text":"44°.","correct":false,"explanation":"This is the remaining angle at $G$, found from $180°-68°-68°=44°$. The requested angle at $F$ equals the given angle at $E$, so it is 68°."},{"text":"112°.","correct":false,"explanation":"This is the supplementary angle to 68°, but no straight-line calculation is needed. Equal sides $EG$ and $FG$ give equal opposite angles at $F$ and $E$, both 68°."},{"text":"56°.","correct":false,"explanation":"This comes from halving the 112° left after subtracting one 68° angle, overlooking that the equal base angles are already determined. The angle at $F$ is 68°."}]},{"id":"a137494f-6077-4746-2fea-d3b5f25257bc","cardType":"basic","points":1,"front":"If outside angle $AEG=112°$ and $AEF$ is a straight line, what is $\\angle GEF$?","back":"68°.","mcqOptions":[{"text":"68°.","correct":true,"explanation":"Angles on a straight line sum to $180°$, so $\\angle GEF=180°-112°=68°$."},{"text":"112°.","correct":false,"explanation":"This incorrectly treats the two adjacent angles as equal. Angles on the straight line $AEF$ sum to $180°$, so $\\angle GEF=180°-112°=68°$."},{"text":"78°.","correct":false,"explanation":"This results from subtracting $112°$ from $190°$ rather than $180°$. Angles on a straight line total $180°$, giving $\\angle GEF=68°$."},{"text":"58°.","correct":false,"explanation":"This results from using $170°$ as the angle total. A straight line contains $180°$, so the missing angle is $180°-112°=68°$."}]},{"id":"c4e1e614-936d-566d-1c04-3ef5a9b3ad38","cardType":"basic","points":1,"front":"If $EF \\parallel GD$ and $FG$ is a transversal, why can $\\angle EFG$ equal $\\angle FGD$?","back":"They are alternate angles.","mcqOptions":[{"text":"They are alternate angles.","correct":true,"explanation":"When a transversal crosses two parallel lines, alternate interior angles are equal. Here, $FG$ crosses the parallel lines $EF$ and $GD$, so the two angles match."},{"text":"They are corresponding angles.","correct":false,"explanation":"Corresponding angles occupy matching positions at the two intersections, which these angles do not. They lie between the parallel lines on opposite sides of the transversal, so they are alternate angles."},{"text":"They are vertically opposite angles.","correct":false,"explanation":"Vertically opposite angles occur across from each other at the same intersection. These angles are at different intersections and are equal because they are alternate angles."},{"text":"They are co-interior angles.","correct":false,"explanation":"Co-interior angles lie on the same side of a transversal and sum to $180°$ rather than generally being equal. These are alternate angles, so they are equal."}]},{"id":"9fce4892-6bfc-9b85-b876-0a7ac1102113","cardType":"basic","points":1,"front":"In triangle $ABE$, $\\angle ABE=54°$ and $\\angle AEB=38°$. Find $\\angle BAE$.","back":"88°.","mcqOptions":[{"text":"88°.","correct":true,"explanation":"The interior angles of a triangle sum to $180°$. Therefore, $\\angle BAE=180°-54°-38°=88°$."},{"text":"92°.","correct":false,"explanation":"This is the sum $54°+38°$, not the remaining angle. Subtracting that sum from the triangle total gives $\\angle BAE=180°-92°=88°$."},{"text":"126°.","correct":false,"explanation":"This subtracts only the $54°$ angle from $180°$ and overlooks the $38°$ angle. Subtracting both known angles gives $\\angle BAE=88°$."},{"text":"142°.","correct":false,"explanation":"This subtracts only the $38°$ angle from $180°$ and ignores the $54°$ angle. Both known angles must be subtracted, giving $\\angle BAE=88°$."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Paper 1"},"heading":"Angles in Parallel Lines","title":"Angles in Parallel Lines Flashcards","topbar":{"backHref":"/gcse/maths/ocr/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"06ef2882-28d6-4edc-80fc-6613667adc48","walled":"$L39"}],"$L3a","$L3b"]