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$\\frac{360}{8} = 45$ M1\n- Final answer $45^\\circ$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Evidence of dividing 360 by 8.","code":"M","acceptable":["360 / 8"]},{"id":"p2","marks":1,"description":"Correct exterior angle.","code":"A"}],"finalAnswers":[],"generatedAt":"2026-05-06T14:00:36.303Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"divide_exterior_angle_sum","label":"Divide the exterior angle sum","steps":[{"type":"text","order":0,"title":"Recall the angle sum","content":"The exterior angles of any polygon add up to $360^\\circ$. Because the octagon is **regular**, all $8$ exterior angles are equal.","highlights":[{"text":"exterior angle of a regular octagon","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{Each exterior angle}=\\color{@sky}{\\htmlData{anchor=division}{\\dfrac{360^\\circ}{8}}}$"},{"latex":"$$\\text{Each exterior angle}=\\color{@green}{\\htmlData{anchor=answer}{45^\\circ}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"division"},{"color":"green","style":"text-color","anchor":"answer"}],"connections":[{"to":"answer","from":"division","color":"sky","label":"evaluate"}]},"order":1,"title":"Divide by eight","description":"Share the total exterior angle equally between the eight sides. The calculation earns M1, and the final value with the degree sign earns A1."}]}],"generatedAt":"2026-07-20T10:44:31.182Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":75},"walkthroughVideo":{"url":"https://assets.mathsgenie.co.uk/walkthroughs/review/521fcbb3-cd8b-43d1-9732-5f68cff52f90.mp4","durationSeconds":58,"posterUrl":"https://assets.mathsgenie.co.uk/walkthroughs/review/521fcbb3-cd8b-43d1-9732-5f68cff52f90.jpg"}},{"id":"16eb6097-71ad-4a58-9329-0365a0d1d7d8","revisionId":"45fe302c-a25b-4fab-baae-fc7cd9713151","questionNumber":null,"questionType":"LA","specification":"","difficultyBand":"easy","tier":null,"totalMarks":2,"sourceTitle":null,"calculatorUse":"non_calc","isCalculation":true,"parts":[{"id":"037dc140-dfb2-4dc5-910a-a0446bedb9be","label":"a","content":"Calculate the size of an exterior angle of a regular decagon.","markscheme":"- Exterior angles of a regular polygon sum to $360^\\circ$. \n- $\\frac{360}{10} = 36$ M1\n- Final answer $36^\\circ$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Evidence of dividing 360 by 10.","code":"M","acceptable":["360 / 10"]},{"id":"p2","marks":1,"description":"Correct exterior angle.","code":"A"}],"finalAnswers":[],"generatedAt":"2026-05-06T14:00:38.155Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"divide_exterior_angle_sum","label":"Divide the exterior angle sum","steps":[{"type":"text","order":0,"title":"Recall the angle sum","content":"The exterior angles of any polygon add up to $360^\\circ$. A decagon has $10$ sides, and because it is **regular**, all $10$ exterior angles are equal.","highlights":[{"text":"exterior angle of a regular decagon","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\dfrac{\\htmlData{anchor=sum}{\\color{@sky}{360^\\circ}}}{10}$"},{"latex":"$$\\htmlData{anchor=answer}{\\color{@green}{36^\\circ}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"sum"},{"color":"green","style":"text-color","anchor":"answer"}],"connections":[{"to":"answer","from":"sum","color":"sky","label":"divide by 10","style":"solid"}]},"order":1,"title":"Divide by ten","description":"Divide the exterior-angle sum equally between the ten sides. The calculation earns M1, and the correct answer of 36° earns A1."}]}],"generatedAt":"2026-07-19T19:25:01.359Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":{"methods":[{"id":"037dc140-dfb2-4dc5-910a-a0446bedb9be:exterior_angle_formula","label":"Using Exterior Angle Formula","steps":[{"type":"text","order":0,"title":"Identify the number of sides","content":"A **decagon** is a polygon with $10$ sides. Since the question specifies it is a **regular** decagon, we know that all its sides are equal in length and all its angles (both interior and exterior) are equal.","highlights":[{"text":"regular decagon","location":"specification"}]},{"type":"text","order":1,"title":"Recall the exterior angle formula","content":"The sum of the exterior angles of any convex polygon is always $360^\\circ$.\n\nBecause a regular decagon has $10$ equal exterior angles, we can find the size of one exterior angle by dividing the total sum ($360^\\circ$) by the number of sides ($n = 10$):\n\n$$\\text{Exterior Angle} = \\frac{360^\\circ}{n}$$"},{"type":"text","order":2,"title":"Calculate the angle size","content":"Substitute $n = 10$ into our formula:\n\n$$\\text{Exterior Angle} = \\frac{360^\\circ}{10} = 36^\\circ$$\n\nWriting down this division earns you the first method mark (\\text{M1})."},{"type":"text","order":3,"title":"State the final answer","content":"The size of an exterior angle of a regular decagon is **$36^\\circ$**.\n\nProviding this correct value earns you the final accuracy mark (\\text{A1})."}]},{"id":"037dc140-dfb2-4dc5-910a-a0446bedb9be:interior_angle_supplement","label":"Via Interior Angle Calculation","steps":[{"type":"text","order":0,"title":"Identify the polygon","content":"A regular decagon is a polygon with $10$ equal sides and $10$ equal interior angles.\n\nFirst, we will find the sum of all the interior angles using the angle sum formula:\n\n$$\\text{Sum of interior angles} = (n - 2) \\times 180^\\circ$$","highlights":[{"text":"regular decagon","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$$n = \\htmlData{anchor=num-sides}{\\color{@sky}{10}}$$"},{"latex":"$$$\\text{Sum} = (\\htmlData{anchor=sub-sides}{\\color{@sky}{10}} - 2) \\times 180^\\circ$$"},{"latex":"$$$\\text{Sum} = 8 \\times 180^\\circ = 1440^\\circ$$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"num-sides"},{"color":"sky","style":"text-color","anchor":"sub-sides"}],"connections":[{"to":"sub-sides","from":"num-sides","color":"sky","label":"substitute n","style":"solid"}]},"order":1,"title":"Find interior angle sum","description":"Substitute $n = 10$ into our formula to calculate the total sum of the interior angles of the decagon."},{"type":"text","order":2,"title":"Calculate one interior angle","content":"Since the decagon is regular, all $10$ of its interior angles are equal. Divide the total sum by $10$ to find the size of one interior angle:\n\n$$\\text{One interior angle} = \\frac{1440^\\circ}{10} = 144^\\circ$$\n\nThis would earn the first method mark **(M1)** for correctly working towards finding the interior angle."},{"type":"text","order":3,"title":"Find the exterior angle","content":"The interior angle and the exterior angle at any vertex lie on a straight line, which means they are supplementary and add up to $180^\\circ$.\n\nSubtract the interior angle from $180^\\circ$ to find the exterior angle:\n\n$$\\text{Exterior angle} = 180^\\circ - 144^\\circ = 36^\\circ$$\n\nThis gives us our final answer of $36^\\circ$ **(A1)**."}]}],"generatedAt":"2026-06-12T10:36:37.508Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":{"percent":67},"walkthroughVideo":{"url":"https://assets.mathsgenie.co.uk/walkthroughs/review/a94abbe0-20d2-43b2-abb3-63272cdda7ea.mp4","durationSeconds":70,"posterUrl":"https://assets.mathsgenie.co.uk/walkthroughs/review/a94abbe0-20d2-43b2-abb3-63272cdda7ea.jpg"}}],"subjectCode":"gcse_maths__ccea","summaries":[{"id":"19613786-4fdd-4638-b732-eeb90102f371","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"296031ce-0bc8-4def-8555-09afb0fc540d","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"4d33c409-f367-4070-81e4-ea261e3f76f2","difficultyBand":"medium","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"5d2e8873-a1ad-4617-8ae4-056b06a97389","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"67528535-e25d-4f1a-a333-4788ce60439c","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"72aee38e-1f6d-401a-b722-49cba51711d1","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"8871d123-e7f3-4bfa-b326-61318547e0de","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"94fc44e8-b4f0-4809-8cb6-9f1a08f4fe38","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"98db4511-c4a1-4577-aa85-0afb9a582380","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"a9ac7a7b-c967-4e94-a247-1e0558279845","difficultyBand":"medium","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"acc2c362-e459-4778-b7ca-48e3cb8c6a20","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"c2374c83-f62f-46c7-91fa-116fd6bdfffa","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"d2612102-4b8a-4468-859b-cd334ed9e156","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"e519e743-7176-4968-8b16-2aff81791a9e","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"9d678c8b-cf5a-482e-a026-274943c17700","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"00133e21-0f8c-4aad-b3d2-02e60ca63891","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"16eb6097-71ad-4a58-9329-0365a0d1d7d8","difficultyBand":"easy","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"3f17b4f3-0b8b-474c-964c-192ef5a375e1","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"49226f8b-e973-4fc9-94c0-c92080475fa9","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"566c5a64-c68a-4c76-8e7c-3c37b7c29084","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"5ae4ba47-37a0-4c20-8b81-f721c9c89bd6","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"5dab90d4-9f02-4d3f-8ec6-81f7f9dc4980","difficultyBand":"medium","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"9de6f436-2d93-46ee-808d-abe66a18d8d1","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"cc60c0ad-6fbc-433e-a1bb-96b8239b34d0","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"de13fcbc-6ebb-4c97-800c-5202e6188879","difficultyBand":"medium","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"e8a41b21-c906-449c-aaec-5d5fc12ac991","difficultyBand":"medium","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"eb77fcc1-47f4-4db3-9948-bcf6577a957e","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"f5739222-41f0-4477-b310-f9148c73e1fd","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"fea21466-b2f8-4496-99d1-daad7682dfe7","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"81ded445-4d11-4b70-97b8-592b90d82180","difficultyBand":"medium","calculatorUse":"non_calc","totalM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in Polygons","topicId":"4e02947d-79fa-8fdd-f540-9b5ada525460","topicSidebar":"$L3a","topicSlug":"grade-4-4-11-angles-in-polygons","topicTitle":"Angles in Polygons"}]}],"$L3b","$L3c"]}]

Angles in Polygons

Question 4

Angles in Polygons Questions

Angles in Polygons

Question 4

Angles in Polygons Questions