6Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"angle_facts","label":"Use angle facts","steps":[{"type":"text","order":0,"title":"Use equal base angles","content":"The triangle is isosceles, so its two base angles are equal. From part (a), one base angle is $62^\\circ$, so the other base angle is also $62^\\circ$."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\color{@sky}{\\htmlData{anchor=eq1}{y+62^\\circ+62^\\circ=180^\\circ}}$"},{"latex":"$$\\color{@amber}{\\htmlData{anchor=eq2}{y=180^\\circ-(62^\\circ+62^\\circ)}}$"},{"latex":"$$\\color{@green}{y=56^\\circ}$"}],"connections":[{"to":"eq2","from":"eq1","color":"sky","style":"solid"}]},"order":1,"title":"Use the angle sum","description":"Angles inside a triangle add to 180°. Subtracting the two known angles from 180° gives the B1 mark."}]}],"generatedAt":"2026-07-19T02:05:03.340Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"34c5dddb-95ae-43e7-8d4a-c77288cdfb43","label":"c","content":"Give reasons for your answer.","markscheme":"- Angles at the base of an isosceles triangle are equal AND angles in a triangle add to $180^\\circ$ B1","marks":1,"order":2,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Provides both required geometric reasons.","code":"B"}],"finalAnswers":[],"generatedAt":"2026-05-05T10:05:14.256Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"angle_reasons","label":"Use angle facts","steps":[{"type":"text","order":0,"title":"Identify the equal angles","content":"The two angles labelled $x$ are equal because **angles at the base of an isosceles triangle are equal**. This is the first reason the examiner requires.","highlights":[{"text":"Give reasons for your answer.","location":"specification"}]},{"type":"text","order":1,"title":"State the second reason","content":"The second reason is that the three interior angles of a triangle add to $180^\\circ$. Together with equal base angles, these are both required for the B1 mark.","highlights":[{"text":"Give reasons for your answer.","location":"specification"}]}]}],"generatedAt":"2026-07-19T02:07:03.722Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"c369008e-1db0-43bd-8d6d-5a9c7f34e2f6","revisionId":"40069e43-a76b-4004-96f7-c723403b1c1b","questionNumber":"14","questionType":"LA","specification":"$$ABC$ is a straight line.\n\n![Triangle ABD with exterior angle 124 at B and angle 68 at D.](https://assets.mathsgenie.co.uk/questions/b0e24dee-7058-45f3-b25b-07e7db3d1f9c.png)","difficulty":2,"difficultyBand":"medium","totalMarks":4,"sourceTitle":"Angles","calculatorUse":"non_calc","parts":[{"id":"0c23d77c-1de7-4897-8623-0f9dddf125a4","label":"0","content":"Show that $ABD$ is an isosceles triangle","markscheme":"- $\\angle ABD = 180 - 124 = 56^\\circ$ M1\n- Reason: Angles on a straight line add to $180^\\circ$ C1\n- $\\angle DAB = 180 - (56 + 68) = 56^\\circ$ M1\n- Conclusion: Two angles are equal ($56^\\circ$), therefore it is an isosceles triangle. C1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Calculates angle ABD = 56.","code":"M"},{"id":"p2","marks":1,"description":"States reason for angle ABD (straight line).","code":"C"},{"id":"p3","marks":1,"description":"Calculates angle DAB = 56.","code":"M"},{"id":"p4","marks":1,"description":"Concludes triangle is isosceles because two angles are equal.","code":"C"}],"finalAnswers":[],"generatedAt":"2026-05-05T10:05:14.256Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"angle_reasoning","label":"Use angle facts","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=abd_sum}{\\color{@sky}{\\angle ABD+124^\\circ=180^\\circ}}$"},{"latex":"$$\\htmlData{anchor=abd_subtract}{\\color{@orange}{\\angle ABD=180^\\circ-124^\\circ}}$"},{"latex":"$$\\htmlData{anchor=abd_result}{\\color{

Angles

Question 14

Angles Questions

Angles

Question 14

Angles Questions