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Work out the size of the angle marked $x$.\n\n![Diagram showing a right angle split into x and 52 degrees.](https://assets.mathsgenie.co.uk/question-image-redraws/sol-max-v1/f5c70828-a463-4b3b-a40f-980bd3465dd8/image-1-03f3f3c37d3b479a9c9af563.svg)","difficulty":1,"difficultyBand":"easy","totalMarks":2,"sourceTitle":"Angles","calculatorUse":"non_calc","isCalculation":true,"parts":[{"id":"9d356fd0-0b79-4af8-bcde-15bb13e4d093","label":"0","content":"","markscheme":"- $90 - 52$ M1\n- $38^\\circ$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Subtracts 52 from 90.","code":"M"},{"id":"p2","marks":1,"description":"Final answer 38.","code":"A"}],"finalAnswers":["38"],"generatedAt":"2026-05-05T10:05:14.256Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"subtract_from_right_angle","label":"Subtract from a right angle","steps":[{"type":"text","order":0,"title":"Use the right angle","content":"Because $AB$ and $BC$ are perpendicular, the angle at $B$ is a right angle, so it measures $90^\\circ$. The two smaller angles, $x$ and $52^\\circ$, split this right angle.","highlights":[{"text":"$$AB$ and $BC$ are perpendicular lines","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$x+\\htmlData{anchor=given}{\\color{@amber}{52^\\circ}}=\\color{@sky}{90^\\circ}$"},{"latex":"$$x=\\color{@sky}{90^\\circ}-\\htmlData{anchor=subtracted}{\\color{@amber}{52^\\circ}}$"}],"highlights":[{"color":"amber","style":"text-color-with-background","anchor":"given"},{"color":"amber","style":"text-color-with-background","anchor":"subtracted"}],"connections":[{"to":"subtracted","from":"given","color":"amber","label":"subtract from both sides"}]},"order":1,"title":"Subtract the known angle","description":"A right angle is $90^\\circ$. The two smaller angles fill it, so take the given angle away. Writing the subtraction earns the method mark (M1)."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$x=\\htmlData{anchor=subtraction}{90^\\circ-52^\\circ}$"},{"latex":"$$x=\\htmlData{anchor=answer}{\\boxed{38^\\circ}}$"}],"connections":[{"to":"answer","from":"subtraction","color":"green","label":"calculate"}]},"order":2,"title":"State the answer","description":"Now carry out the subtraction and include the degree symbol. This earns the accuracy mark (A1)."}]}],"generatedAt":"2026-07-19T02:09:08.165Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"5a3c696b-17f2-4437-8036-20b4dbd8e633","revisionId":"378be0cb-bd66-4621-a722-fcb5391cc4e2","questionNumber":"7","questionType":"LA","specification":"$$ABC$ is an isosceles triangle. Work out the size of the angle marked $x$.\n\n![Isosceles triangle with base angle 65 degrees.](https://assets.mathsgenie.co.uk/question-image-redraws/sol-max-v2/5a3c696b-17f2-4437-8036-20b4dbd8e633/image-1-898bacb157a60222dc4348d2.svg)","difficulty":1,"difficultyBand":"easy","totalMarks":2,"sourceTitle":"Angles","calculatorUse":"non_calc","isCalculation":true,"parts":[{"id":"1e11d7e7-4c76-4f9b-84cb-09df7a7be2e2","label":"0","content":"","markscheme":"- $65 + 65 = 130$ M1\n- $180 - 130 = 50^\\circ$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Identifies base angles are equal and sums them ($65 + 65$).","code":"M"},{"id":"p2","marks":1,"description":"Subtracts sum from 180 to find 50.","code":"A"}],"finalAnswers":["50"],"generatedAt":"2026-05-05T10:05:14.256Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"equal_angles_then_subtract","label":"Use equal base angles","steps":[{"type":"text","order":0,"title":"Identify equal angles","content":"The matching marks show that $AB=AC$. Therefore the angles opposite these equal sides, at $B$ and $C$, are equal. Since the angle at $B$ is $65^\\circ$, the angle at $C$ is also $65^\\circ$.","highlights":[{"text":"$$ABC$ is an isosceles triangle.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=base_angles}{\\color{@sky}{65^\\circ+65^\\circ}}$"},{"latex":"$$\\htmlData{anchor=base_total}{\\color{@sky}{130^\\circ}}$"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"base_angles"}],"connections":[{"to":"base_total","from":"base_angles","color":"sky","label":"add"}]},"order":1,"title":"Add base angles","description":"Add the two equal base angles. This calculation earns the method mark (M1)."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$x=\\htmlData{anchor=subtraction}{180^\\circ-130^\\circ}$"},{"latex":"$$\\htmlData{anchor=result}{x=50^\\circ}$"}],"highlights":[{"color":"amber","style":"text-color","anchor":"subtraction"},{"color":"green","style":"text-color-with-background","anchor":"result"}],"connections":[{"to":"result","from":"subtraction","color":"green","label":"calculate"}]},"order":2,"title":"Find remaining angle","description":"Use the angle sum of a triangle, then subtract the total of the two base angles. The correct final angle earns A1."}]}],"generatedAt":"2026-07-19T18:55:36.181Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":{"methods":[{"id":"1e11d7e7-4c76-4f9b-84cb-09df7a7be2e2:arithmetic","label":"Arithmetic Calculation","steps":[{"type":"text","order":0,"title":"Identify equal angles","content":"An **isosceles triangle** has two equal sides and two equal base angles.\n\nFrom the markings on the triangle, we can see that the two sides meeting at the top vertex are equal in length. This means the two angles at the base are equal. \n\nSince one of the base angles is given as $65^\\circ$, the other base angle must also be $65^\\circ$."},{"type":"text","order":1,"title":"Sum the base angles","content":"Next, let's calculate the sum of these two equal base angles:\n\n$$65^\\circ + 65^\\circ = 130^\\circ$$\n\n*(This step earns the first method mark, **M1**)*"},{"type":"text","order":2,"title":"Find angle x","content":"We know that the angles in any triangle always add up to $180^\\circ$.\n\nTo find the size of the angle marked $x$, we subtract the sum of the base angles from $180^\\circ$:\n\n$$x = 180^\\circ - 130^\\circ = 50^\\circ$$\n\n*(This completes the calculation to earn the accuracy mark, **A1**)*"}]},{"id":"1e11d7e7-4c76-4f9b-84cb-09df7a7be2e2:algebraic","label":"Algebraic Equation","steps":[{"type":"text","order":0,"title":"Identify equal angles","content":"The question states that $ABC$ is an **isosceles triangle**.\n\nAn isosceles triangle has two equal sides and two equal base angles. Looking at the markings on the diagram, the two base angles are equal. \n\nSince one of the base angles is given as $65^\\circ$, the other base angle must also be $65^\\circ$."},{"type":"hyper_latex","block":{"nodes":[{"text":"The sum of all interior angles in any triangle is always $180^\\circ$. We can write this as an algebraic equation:"},{"latex":"$$\\htmlData{anchor=angle-x}{\\color{@sky}{x}} + \\htmlData{anchor=base-1}{\\color{@amber}{65^\\circ}} + \\htmlData{anchor=base-2}{\\color{@amber}{65^\\circ}} = \\htmlData{anchor=total}{\\color{@purple}{180^\\circ}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"angle-x"},{"color":"amber","style":"text-color","anchor":"base-1"},{"color":"amber","style":"text-color","anchor":"base-2"},{"color":"purple","style":"text-color","anchor":"total"}],"connections":[{"to":"base-2","from":"base-1","color":"amber","label":"equal angles","style":"solid"}]},"order":1,"title":"Set up the equation","description":"We establish a linear equation where the sum of $x$ and the two base angles of $65^\\circ$ equals $180^\\circ$."},{"type":"text","order":2,"title":"Simplify the equation","content":"First, we add the two known angles together:\n\n$$65 + 65 = 130$$\n\nNow, substitute this back into our equation:\n\n$$x + 130 = 180$$\n\n*This step earns the first method mark (\\mathbf{M1}) in the markscheme.*"},{"type":"text","order":3,"title":"Solve for x","content":"To isolate $x$, subtract $130$ from both sides of the equation:\n\n$$\\begin{aligned} x &= 180 - 130 \\\\ x &= 50^\\circ \\end{aligned}$$\n\n*This final calculation earns the accuracy mark (\\mathbf{A1}).*\n\nTherefore, the size of the angle marked $x$ is **$50^\\circ$**."}]}],"generatedAt":"2026-06-12T17:06:38.783Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"fa295aae-8afc-4e8b-b521-9e0648c3d29a","revisionId":"86aedbbe-636a-40a2-a96b-3bbca900f18b","questionNumber":"8","questionType":"LA","specification":"![Diagram showing angles on a straight line, x and 132 degrees.](https://assets.mathsgenie.co.uk/question-image-redraws/sol-max-v1/fa295aae-8afc-4e8b-b521-9e0648c3d29a/image-1-0ee32df3440a75ddf7e71058.svg)","difficulty":1,"difficultyBand":"easy","totalMarks":2,"sourceTitle":"Angles","calculatorUse":"non_calc","isCalculation":true,"parts":[{"id":"b2e5f6ac-1d80-4d9f-9487-e66827370bf2","label":"a","content":"Work out the size of the angle marked $x$.","markscheme":"- $180 - 132 = 48^\\circ$ B1","marks":1,"order":0,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Correctly calculates $x = 48$.","code":"B"}],"finalAnswers":["48"],"generatedAt":"2026-05-05T10:05:14.256Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"angles_on_a_straight_line","label":"Angles on a straight line","steps":[{"type":"text","order":0,"title":"Recall the angle fact","content":"Angles on a straight line add up to $180^\\circ$. The diagram shows that $x$ and $132^\\circ$ are adjacent angles forming a straight line, so together they total $180^\\circ$.","highlights":[{"text":"Work out the size of the angle marked $x$.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$x+132^\\circ=\\color{@sky}{\\htmlData{anchor=total}{180^\\circ}}$"},{"latex":"$$x=\\color{@sky}{\\htmlData{anchor=subtraction}{180^\\circ-132^\\circ}}$"},{"latex":"$$x=48^\\circ$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"total"},{"color":"sky","style":"text-color","anchor":"subtraction"}],"connections":[{"to":"subtraction","from":"total","color":"sky","label":"subtract 132 degrees"}]},"order":1,"title":"Subtract the known angle","description":"Subtract the known angle from the straight-line total. The calculation 180° − 132° = 48° earns the one mark."}]}],"generatedAt":"2026-07-19T16:56:21.113Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"1f6f3820-b36e-4c18-9a56-b3d49a4e1edd","label":"b","content":"Give a reason for your answer.","markscheme":"- Angles on a straight line add to $180^\\circ$ B1","marks":1,"order":1,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"States that angles on a straight line sum to 180 degrees.","code":"B"}],"finalAnswers":[],"generatedAt":"2026-05-05T10:05:14.256Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"straight_line_reason","label":"Use the straight-line rule","steps":[{"type":"text","order":0,"title":"Identify the line","content":"The angles labelled $x$ and $132^\\circ$ are adjacent angles above the same straight line.","highlights":[{"text":"Give a reason for your answer.","location":"specification"}]},{"type":"text","order":1,"title":"State the reason","content":"Write: **Angles on a straight line add to $180^\\circ$.** This exact angle fact earns the **B1 mark**."}]}],"generatedAt":"2026-07-19T16:57:15.721Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null}],"subjectCode":"gcse_maths","summaries":[{"id":"4fe0ce56-8606-4ab8-b705-f9e5419d1d0b","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":1,"questionType":"LA","isCalculation":false},{"id":"552b2cc4-39be-4258-a6ea-f6235bc1c95d","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":1,"questionType":"LA","isCalculation":false},{"id":"c519db2a-9077-4b51-b952-b3c63596bfae","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"516d1fe3-8cfb-4bd6-ae90-1ec6fe1a2ec6","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":1,"questionType":"LA","isCalculation":false},{"id":"39717d19-7e89-4142-add3-7063f2bfb9d2","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":1,"questionType":"LA","isCalculation":false},{"id":"4172501d-9c7c-4383-bd8e-4f011fe1005d","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"4f229e13-6f55-4ac4-b678-7e3031076da0","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":1,"questionType":"LA","isCalculation":false},{"id":"925da1bf-89c0-47ff-8733-87da6fce81f6","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"b9c7a426-3cc7-4bd9-b9aa-bb2c12da4b3c","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"c451d101-18f1-4a40-b48a-24d52d2ca5de","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"f9d420bc-2783-4d13-80fb-396a27541ab9","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"ab9a072b-3e00-4684-9566-bf7cf80f06f5","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":1,"questionType":"LA","isCalculation":false},{"id":"1702b49f-f6bd-4382-937f-8f7fcfce6196","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"5ff005bf-704c-4ed0-bab4-e41425d8f525","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"b136dad8-4851-4898-9ede-c216c6c95391","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"b7e5e68e-6097-4589-a75a-424308d9d22d","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":1,"questionType":"LA","isCalculation":false},{"id":"f9d8947f-7877-4d32-8759-9de6fe925bc0","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":1,"questionType":"LA","isCalculation":false},{"id":"0787502d-dc64-4e4a-a515-1ac132a03b83","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"f5c70828-a463-4b3b-a40f-980bd3465dd8","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"5a3c696b-17f2-4437-8036-20b4dbd8e633","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"fa295aae-8afc-4e8b-b521-9e0648c3d29a","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"0b525798-3060-4b48-8540-a5464043e7cd","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"07a712ec-993a-4df1-af99-2c843930e58a","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"a6454e73-0734-486c-95d4-df33cf26ddda","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"1076a56b-692c-4491-9c91-72780605c9e0","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"fdf48a6c-0bf2-4a89-a88d-50818f6174ee","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"c369008e-1db0-43bd-8d6d-5a9c7f34e2f6","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true}],"title":"Angles","topicId":"6362325b-dd27-49b1-a525-93b90580475e","topicSidebar":"$L3b","topicSlug":"grade-2-2-10-angles","topicTitle":"Angles"}]}],"$L3c","$L3d"]}]

Angles

Question 12

Angles Questions

Angles

Question 12

Angles Questions