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even when extended indefinitely in both directions."},{"text":"Parallel lines stay different distances apart and never meet.","correct":false,"explanation":"Lines whose separation changes are not parallel, even if they never meet in the part of the diagram shown. Parallel lines stay the same distance apart and never meet."},{"text":"Parallel lines stay the same distance apart and eventually meet.","correct":false,"explanation":"Meeting lines cannot be parallel because parallel lines do not intersect, however far they are extended. Parallel lines stay the same distance apart and never meet."},{"text":"Parallel lines stay closer and closer together and eventually meet.","correct":false,"explanation":"Getting closer and eventually meeting describes converging lines, not parallel lines. Parallel lines maintain the same separation and never meet when extended."}]},{"id":"d691bb39-4198-4617-8f1a-a879117bb8b1","cardType":"cloze","points":null,"front":"A transversal is a line that [ ].","back":"A transversal is a line that crosses two or more other lines.","mcqOptions":[{"text":"crosses two or more other lines","correct":true,"explanation":"A transversal intersects at least two other lines at distinct points, creating the angle relationships used when those lines are parallel."},{"text":"crosses exactly one other line","correct":false,"explanation":"Crossing only one line does not create the two intersections needed for transversal angle relationships. A transversal crosses two or more other lines."},{"text":"runs parallel to two other lines","correct":false,"explanation":"Running parallel means the line does not intersect the other lines, whereas a transversal must cross two or more other lines."},{"text":"meets two other lines at one point","correct":false,"explanation":"Passing through a shared intersection is not the usual transversal arrangement because it does not create separate crossings. A transversal crosses two or more other lines."}]},{"id":"5af0b8e7-0b28-47a8-be4f-f1f6195b1571","cardType":"basic","points":1,"front":"An angle next to 68° on a straight line is what?","back":"112°.","mcqOptions":[{"text":"112°.","correct":true,"explanation":"Adjacent angles on a straight line sum to 180°, so the missing angle is $180° - 68° = 112°$."},{"text":"68°.","correct":false,"explanation":"This repeats the given angle instead of using the straight-line total. Adjacent angles on a straight line sum to 180°, giving $180° - 68° = 112°$."},{"text":"122°.","correct":false,"explanation":"This subtracts 68° from 190° rather than the straight-line total of 180°. The required angle is $180° - 68° = 112°$."},{"text":"292°.","correct":false,"explanation":"This uses the reflex-angle total of 360° instead of the 180° total for a straight line. The adjacent angle is $180° - 68° = 112°$."}]},{"id":"df0778da-04f1-4b01-98c7-bbe39c666e74","cardType":"basic","points":1,"front":"The angle vertically opposite 68° is what?","back":"68°.","mcqOptions":[{"text":"68°.","correct":true,"explanation":"Vertically opposite angles are equal, so the angle directly opposite the given 68° angle also measures 68°."},{"text":"112°.","correct":false,"explanation":"112° is the supplementary angle adjacent to 68°, found using a straight-line total. The vertically opposite angle is equal to 68°."},{"text":"136°.","correct":false,"explanation":"This incorrectly doubles the given angle. Vertically opposite angles are equal rather than added together, so the required angle is 68°."},{"text":"22°.","correct":false,"explanation":"This subtracts the angle from 90°, confusing vertically opposite angles with complementary angles. Vertically opposite angles are equal, so the answer is 68°."}]},{"id":"83b8d114-daa2-4bf8-a578-1b68a42d226d","cardType":"cloze","points":null,"front":"Angles in a triangle add to [ ].","back":"Angles in a triangle add to 180°.","mcqOptions":[{"text":"180°","correct":true,"explanation":"The three interior angles of every triangle have a total of 180°, regardless of the triangle’s side lengths or shape."},{"text":"360°","correct":false,"explanation":"360° is the interior-angle total for a quadrilateral, not a triangle. The three interior angles of a triangle add to 180°."},{"text":"90°","correct":false,"explanation":"90° is the size of one right angle, not the total for every triangle. A triangle’s three interior angles add to 180°."},{"text":"270°","correct":false,"explanation":"270° can result from counting three right angles, but a triangle cannot contain three right angles. Its interior angles always total 180°."}]},{"id":"b3a3fffc-bcd5-4a0c-99c0-cd9c9cd1acc6","cardType":"basic","points":1,"front":"When parallel lines are cut by a transversal, what is true of corresponding angles?","back":"Corresponding angles are equal.","mcqOptions":[{"text":"Corresponding angles are equal.","correct":true,"explanation":"For parallel lines, corresponding angles occupy the same relative position at the two intersections and therefore have equal measures."},{"text":"Corresponding angles add to 180°.","correct":false,"explanation":"Adding to 180° is the relationship for co-interior angles, not corresponding angles. When the lines are parallel, corresponding angles are equal."},{"text":"Corresponding angles are vertically opposite.","correct":false,"explanation":"Vertically opposite angles occur at the same intersection, whereas corresponding angles occur at different intersections. Corresponding angles are equal when the lines are parallel."},{"text":"Corresponding angles are unequal.","correct":false,"explanation":"Corresponding angles may look separated in the diagram, but parallel lines ensure that angles in matching positions are equal, not unequal."}]},{"id":"e6d4e5c3-60f3-4bee-89c7-21a8c58999d3","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":"Corresponding angles occupy matching locations around their two intersections, such as top-right at each crossing, so they are in the same relative position."},{"text":"opposite relative position","correct":false,"explanation":"An opposite relative position identifies a different angle relationship rather than corresponding angles. Corresponding angles occupy the same relative position at each crossing."},{"text":"alternate relative position","correct":false,"explanation":"Alternate positions are associated with alternate angles, which lie on opposite sides of the transversal. Corresponding angles occupy the same relative position at each crossing."},{"text":"vertically opposite position","correct":false,"explanation":"Vertically opposite angles are across from each other at one intersection, not at matching positions across two intersections. Corresponding angles use the same relative position."}]},{"id":"318bee27-e376-4efd-b916-b70aabcc01c3","cardType":"basic","points":1,"front":"A top-right angle is 74°. The top-right corresponding angle is $x$. What is $x$?","back":"$x = 74^\\circ$.","mcqOptions":[{"text":"$x = 74^\\circ$.","correct":true,"explanation":"Corresponding angles formed by a transversal crossing parallel lines are equal. Since both angles occupy the top-right position, $x = 74^\\circ$."},{"text":"$x = 106^\\circ$.","correct":false,"explanation":"This uses the supplementary-angle calculation $180^\\circ - 74^\\circ$, which applies to co-interior or adjacent angles. Corresponding angles are equal, so $x = 74^\\circ$."},{"text":"$x = 148^\\circ$.","correct":false,"explanation":"This doubles the given angle, but corresponding angles are not added together. Their matching positions make them equal, so $x = 74^\\circ$."},{"text":"$x = 16^\\circ$.","correct":false,"explanation":"This subtracts 74° from 90°, confusing the pair with complementary angles. Corresponding angles are equal, so $x = 74^\\circ$."}]},{"id":"7b6af190-c7ad-4ec1-9880-58d7b3c09682","cardType":"cloze","points":null,"front":"Alternate angles lie [ ] and on [ ].","back":"Alternate angles lie between the parallel lines and on opposite sides of the transversal.","mcqOptions":[{"text":"Alternate angles lie between the parallel lines and on opposite sides of the transversal.","correct":true,"explanation":"Alternate angles are the interior pair formed between the two parallel lines, with one angle lying on each side of the transversal."},{"text":"Alternate angles lie between the parallel lines and on the same side of the transversal.","correct":false,"explanation":"Angles between the parallel lines on the same side of the transversal are co-interior angles. Alternate angles are between the lines on opposite sides of the transversal."},{"text":"Alternate angles lie in corresponding positions and on the same side of the transversal.","correct":false,"explanation":"Angles in matching positions on the same side are corresponding angles, not alternate angles. Alternate angles lie between the parallel lines on opposite sides of the transversal."},{"text":"Alternate angles lie outside the parallel lines and on the same side of the transversal.","correct":false,"explanation":"This describes same-side exterior angles rather than alternate angles. Alternate angles lie between the parallel lines and on opposite sides of the transversal."}]},{"id":"2639d433-03be-481c-91e2-5ebc50eb62a6","cardType":"basic","points":1,"front":"When parallel lines are cut by a transversal, what is true of alternate angles?","back":"Alternate angles are equal.","mcqOptions":[{"text":"Alternate angles are equal.","correct":true,"explanation":"For two parallel lines cut by a transversal, alternate angles form a matching pair on opposite sides of the transversal, so they have equal measures."},{"text":"Alternate angles are supplementary.","correct":false,"explanation":"Supplementary angles add to 180°, which is the rule for co-interior angles. Alternate angles formed by a transversal across parallel lines are equal."},{"text":"Alternate angles differ by 90°.","correct":false,"explanation":"A 90° difference is not a parallel-line angle rule. When a transversal crosses parallel lines, each pair of alternate angles has equal measures."},{"text":"Alternate angles add to 360°.","correct":false,"explanation":"Angles around a point add to 360°, but this does not describe a pair of alternate angles. Alternate angles between parallel lines are equal."}]},{"id":"afcb868f-9de7-4f73-96e1-290d09cc7d55","cardType":"basic","points":1,"front":"One alternate angle is 49°. What is the other alternate angle?","back":"49°.","mcqOptions":[{"text":"49°.","correct":true,"explanation":"Alternate angles formed when a transversal crosses parallel lines are equal. Therefore, an angle alternate to 49° must also measure 49°."},{"text":"131°.","correct":false,"explanation":"Subtracting 49° from 180° gives 131°, but that supplementary calculation applies to co-interior angles. Alternate angles are equal, so the other angle is 49°."},{"text":"41°.","correct":false,"explanation":"Subtracting from 90° incorrectly assumes the angles are complementary. Alternate angles across parallel lines are equal, so the other angle is 49°."},{"text":"98°.","correct":false,"explanation":"Doubling 49° does not follow any alternate-angle rule. Since alternate angles between parallel lines are equal, the required angle remains 49°."}]},{"id":"c5f4d878-db0f-41ba-ad2f-22af05d4d30d","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 and on the same side of the transversal. Their measures consequently add to 180°."},{"text":"opposite side","correct":false,"explanation":"Angles on opposite sides of the transversal are associated with the alternate-angle pattern. Co-interior angles instead lie on the same side of the transversal."},{"text":"left side","correct":false,"explanation":"The definition does not depend on a fixed left-hand position, since a diagram can be rotated. Co-interior angles are on the same side of the transversal."},{"text":"right side","correct":false,"explanation":"The right-hand position is not part of the definition and changes if the diagram is rotated. Co-interior angles lie on the same side of the transversal."}]},{"id":"bfb4c069-0b0c-43c5-9e54-c0417b0b0ee0","cardType":"basic","points":1,"front":"What is true of co-interior angles on parallel lines?","back":"Co-interior angles add to 180°.","mcqOptions":[{"text":"Co-interior angles add to 180°.","correct":true,"explanation":"Co-interior angles lie on the same side of a transversal between two parallel lines. They are supplementary, meaning their measures have a total of 180°."},{"text":"Co-interior angles are equal.","correct":false,"explanation":"Equality is the rule for alternate and corresponding angles, not generally for co-interior angles. Co-interior angles are supplementary and therefore add to 180°."},{"text":"Co-interior angles add to 90°.","correct":false,"explanation":"A total of 90° describes complementary angles, not co-interior angles. Co-interior angles on parallel lines are supplementary, so they add to 180°."},{"text":"Co-interior angles add to 360°.","correct":false,"explanation":"A total of 360° applies to angles around a point, not a co-interior pair. Co-interior angles between parallel lines add to 180°."}]},{"id":"573b020f-a882-462d-99a6-d6cdc385255b","cardType":"basic","points":1,"front":"If co-interior angles are 113° and $x$, what equation should you write?","back":"$x + 113^\\circ = 180^\\circ$.","mcqOptions":[{"text":"$x + 113^\\circ = 180^\\circ$.","correct":true,"explanation":"Co-interior angles on parallel lines are supplementary, so their measures must total 180°. Adding the unknown angle to 113° gives the required equation."},{"text":"$x = 113^\\circ$.","correct":false,"explanation":"Setting the angles equal confuses co-interior angles with alternate or corresponding angles. Co-interior angles add to 180°, so the equation is $x + 113^\\circ = 180^\\circ$."},{"text":"$x + 113^\\circ = 90^\\circ$.","correct":false,"explanation":"Using 90° incorrectly treats the two angles as complementary. Co-interior angles are supplementary, so the correct equation is $x + 113^\\circ = 180^\\circ$."},{"text":"$x - 113^\\circ = 180^\\circ$.","correct":false,"explanation":"Subtracting the two angle measures does not express their supplementary relationship. Their sum is 180°, giving the equation $x + 113^\\circ = 180^\\circ$."}]},{"id":"81cfc2cb-99b9-41dc-8c41-bca588b1bfed","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 on parallel lines add to 180°. Subtracting gives $180^\\circ - 118^\\circ = 62^\\circ$, so the other angle is 62°."},{"text":"118°.","correct":false,"explanation":"Repeating 118° incorrectly applies the equality rule for alternate or corresponding angles. Co-interior angles add to 180°, so the other angle is 62°."},{"text":"72°.","correct":false,"explanation":"This results from using 190° as the supplementary total instead of 180°. The correct calculation is $180^\\circ - 118^\\circ = 62^\\circ$."},{"text":"68°.","correct":false,"explanation":"This results from subtracting 112° rather than the given 118°, an easy digit-reading slip. Using 118° correctly gives $180^\\circ - 118^\\circ = 62^\\circ$."}]},{"id":"b0d61099-d9aa-40d0-a704-cc12b43f6213","cardType":"basic","points":1,"front":"An exterior 118° angle is on a straight line with a triangle’s inside angle. What is the inside angle?","back":"62°.","mcqOptions":[{"text":"62°.","correct":true,"explanation":"The exterior angle and adjacent inside angle form a straight line, so they total 180°. Therefore, the inside angle is $180^\\circ - 118^\\circ = 62^\\circ$."},{"text":"118°.","correct":false,"explanation":"Using the same measure confuses this pair with equal alternate angles. Adjacent angles on a straight line sum to 180°, so the inside angle is 62°."},{"text":"72°.","correct":false,"explanation":"This comes from incorrectly using 190° as the angle total for a straight line. The correct total is 180°, giving $180^\\circ - 118^\\circ = 62^\\circ$."},{"text":"59°.","correct":false,"explanation":"Halving the exterior angle does not find its adjacent angle. The two angles form a straight line, so subtraction from 180° gives 62°."}]},{"id":"8b1156b5-b8ff-4729-bd20-1aaed006f775","cardType":"basic","points":1,"front":"A triangle has angles 38° and 62°. What is the third angle?","back":"80°.","mcqOptions":[{"text":"80°.","correct":true,"explanation":"The interior angles of a triangle total 180°. Since 38° + 62° = 100°, the remaining angle is 180° - 100° = 80°."},{"text":"100°.","correct":false,"explanation":"This uses the sum of the two given angles as the missing angle. Triangle angles total 180°, so subtracting 100° gives the correct angle of 80°."},{"text":"90°.","correct":false,"explanation":"This incorrectly assumes the third angle is a right angle. The angle sum is 180°, and 180° - 38° - 62° gives 80°."},{"text":"76°.","correct":false,"explanation":"This comes from doubling the 38° angle rather than using the triangle angle sum. Subtracting both given angles from 180° gives 80°."}]},{"id":"0a28dfa1-0681-4617-b7a5-f8c31c3a6c05","cardType":"basic","points":1,"front":"What property of a parallelogram lets you use parallel-line angle facts on its sides?","back":"Opposite sides are parallel.","mcqOptions":[{"text":"Opposite sides are parallel.","correct":true,"explanation":"A parallelogram has two pairs of opposite sides that are parallel. These parallel sides allow corresponding, alternate and co-interior angle facts to be applied."},{"text":"Adjacent sides are equal.","correct":false,"explanation":"Adjacent sides are not generally equal in a parallelogram; that is a property of a rhombus. Parallel-line angle facts apply because opposite sides are parallel."},{"text":"Diagonals are perpendicular.","correct":false,"explanation":"Perpendicular diagonals are a property of some special parallelograms, such as rhombuses, but not all parallelograms. The relevant property is that opposite sides are parallel."},{"text":"All angles are equal.","correct":false,"explanation":"All angles are equal only in rectangular parallelograms, not in every parallelogram. Parallel-line angle rules can be used because opposite sides are parallel."}]},{"id":"c6cba7fa-1316-461b-b096-cc4315fd29de","cardType":"basic","points":1,"front":"Angle BAD is 124° and is co-interior with angle ABE. What is angle ABE?","back":"56°.","mcqOptions":[{"text":"56°.","correct":true,"explanation":"Co-interior angles between parallel lines sum to 180°. Therefore angle ABE is 180° - 124° = 56°."},{"text":"124°.","correct":false,"explanation":"This treats co-interior angles as equal, confusing them with corresponding or alternate angles. Co-interior angles sum to 180°, so angle ABE is 56°."},{"text":"66°.","correct":false,"explanation":"This results from subtracting 124° from 190° rather than 180°. Co-interior angles are supplementary, so the correct calculation gives 56°."},{"text":"46°.","correct":false,"explanation":"This results from subtracting 124° from 170°, using the wrong total. Co-interior angles sum to 180°, giving angle ABE as 56°."}]},{"id":"fd49aea6-cb7e-4f89-a6d1-25f6ab223d5b","cardType":"cloze","points":null,"front":"In an isosceles triangle, angles opposite [ ] are [ ].","back":"In an isosceles triangle, angles opposite equal sides are equal.","mcqOptions":[{"text":"In an isosceles triangle, angles opposite equal sides are equal.","correct":true,"explanation":"An isosceles triangle has two equal sides. The angles opposite those equal sides are the two equal base angles."},{"text":"In an isosceles triangle, angles opposite unequal sides are equal.","correct":false,"explanation":"Unequal sides have unequal opposite angles, not equal ones. In an isosceles triangle, it is the angles opposite the equal sides that are equal."},{"text":"In an isosceles triangle, angles opposite equal sides are supplementary.","correct":false,"explanation":"The base angles of an isosceles triangle are equal rather than supplementary. They are the angles opposite the triangle’s equal sides."},{"text":"In an isosceles triangle, angles opposite unequal sides are supplementary.","correct":false,"explanation":"This combines two incorrect claims: unequal sides do not have equal opposite angles, and those angles are not necessarily supplementary. Angles opposite equal sides are equal."}]},{"id":"86cdf154-3c93-41ed-ba10-2ee06efcbea6","cardType":"basic","points":1,"front":"If EG = FG in triangle EFG, which base angles are equal?","back":"Angles at E and F.","mcqOptions":[{"text":"Angles at E and F.","correct":true,"explanation":"Equal sides have equal opposite angles. Side EG is opposite the angle at F, while side FG is opposite the angle at E, so those angles are equal."},{"text":"Angles at E and G.","correct":false,"explanation":"The angle at G lies between the two equal sides and is the vertex angle, not a base angle. The equal base angles are at E and F."},{"text":"Angles at F and G.","correct":false,"explanation":"The angle at G is the vertex angle between EG and FG, so it is not one of the equal base angles. The equal angles are at E and F."},{"text":"Both angles at G.","correct":false,"explanation":"This incorrectly repeats the vertex angle rather than identifying the two base angles. Because EG = FG, the opposite angles at F and E are equal."}]},{"id":"1d4fcee7-4094-477e-b625-848f2cd4f2f4","cardType":"basic","points":1,"front":"Angle at F is 76° and $x$ is alternate to it. What is $x$?","back":"$x = 76^\\circ$.","mcqOptions":[{"text":"$x = 76^\\circ$.","correct":true,"explanation":"Alternate angles formed when a transversal crosses parallel lines are equal. Since the angle at F is 76°, its alternate angle is also 76°."},{"text":"$x = 104^\\circ$.","correct":false,"explanation":"This incorrectly treats the alternate angle as supplementary. Alternate angles are equal, so $x$ has the same value as the angle at F: $76^\\circ$."},{"text":"$x = 38^\\circ$.","correct":false,"explanation":"This halves the given angle, but alternate angles are copied directly rather than divided. Since they are equal, $x = 76^\\circ$."},{"text":"$x = 90^\\circ$.","correct":false,"explanation":"This assumes the alternate angle must be a right angle. Alternate angles are equal when the lines are parallel, so $x = 76^\\circ$."}]}]}],"examCountdown":null,"heading":"Angles in Parallel Lines","title":"Angles in Parallel Lines Flashcards","topbar":{"backHref":"/igcse/maths/oxford-aqa/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"e030477e-5376-4c56-995f-c6a74b14144f","walled":"$L39"}],"$L3a","$L3b"]