Angles – Parallel Lines – Higher – GCSE Questions – AQA These questions are the same format as previous GCSE exams. COPY means they use the exact same numbers as the original GCSE question. Otherwise, they are clone questions using different numbers. The worksheets are provided in 2 sizes.

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AQA Higher: November 2017 Paper 3, Q8 ABCD is a parallelogram. AE = AC 1 ABCD is a parallelogram. AE = AC Not drawn accurately Not drawn accurately A E B A E B 𝑥 𝑥 148.5° 148.5° 5𝑥 5𝑥 C D C D Work out the size of angle 𝑥. Work out the size of angle 𝑥. [4 marks] [4 marks] Answer degrees Answer degrees

AQA Higher: November 2017 Paper 1, Q19 The diagram shows a triangle and a trapezium. 1 The diagram shows a triangle and a trapezium. [3 marks] [3 marks] 115° Prove that 𝑎 = 𝑏 𝑎 Prove that 𝑎 = 𝑏 𝑎 115° 65° 65° 𝑐 𝑐 𝑏 𝑏 AQA Higher: November 2017 Paper 1, Q19 AQA Higher: November 2017 Paper 1, Q19 1 The diagram shows a triangle and a trapezium. 1 The diagram shows a triangle and a trapezium. [3 marks] [3 marks] Prove that 𝑎 = 𝑏 𝑎 115° 𝑎 115° Prove that 𝑎 = 𝑏 65° 65° 𝑐 𝑐 𝑏 𝑏

AQA Higher: June 2017 Paper 3, Q10 AQA Higher: June 2017 Paper 3, Q10 AF, BC and DF are straight lines. 1 AF, BC and DF are straight lines. D D B B A 𝑤 A 𝑤 𝑧 F F 8𝑥−20° 8𝑥−20° 𝑧 4𝑥+60° 4𝑥+60° C C E E 1 (a) Josh assumes that BC and DE are parallel. What answer should she get for the size of angle 𝑧? 1 (a) Josh assumes that BC and DE are parallel. What answer should she get for the size of angle 𝑧? [4 marks] [4 marks] Answer degrees Answer degrees 1 (b) In fact, AB and CD are not parallel angle 𝑤 is 130° What effect does this have on the size of angle 𝑧? Tick a box. 1 (b) In fact, AB and CD are not parallel angle 𝑤 is 130° What effect does this have on the size of angle 𝑧? Tick a box. 𝑧 is bigger 𝑧 is the same 𝑧 is smaller 𝑧 is bigger 𝑧 is the same 𝑧 is smaller Show working to support your answer. Show working to support your answer. [3 marks] [3 marks]

AQA Higher: November 2017 Paper 3, Q8 ABCD is a parallelogram. AE = AC Not drawn accurately A E B 𝑥 148.5° 5𝑥 C D Work out the size of angle 𝑥. [4 marks] Answer degrees

AQA Higher: June 2017 Paper 3, Q10 AF, BC and DF are straight lines. D B A 𝑤 F 8𝑥−20° 𝑧 4𝑥+60° C E 1 (a) Josh assumes that BC and DE are parallel. What answer should she get for the size of angle 𝑧? [4 marks] Answer degrees 1 (b) In fact, AB and CD are not parallel angle 𝑤 is 130° What effect does this have on the size of angle 𝑧? Tick a box. 𝑧 is bigger 𝑧 is the same 𝑧 is smaller Show working to support your answer. [3 marks]

AQA Higher: November 2017 Paper 3, Q8 ABCD is a parallelogram. AE = AC Not drawn accurately 31.5° A E B 117° 𝑥 148.5° 5𝑥 31.5° C D Work out the size of angle 𝑥. [4 marks] AEC = 180 – 148.5 = 31.5 ACE = 31.5 CAE = 180 – (2 × 31.5) = 117 CAE + ABD = 180 (co-interior angles total 180°) ABD = 180 – 117 = 63 6𝑥 = 63 𝑥 = 63 ÷ 6 = 10.5 10.5 Answer degrees

AQA Higher: June 2017 Paper 3, Q10 AF, BC and DF are straight lines. D B A 𝑤 F 8𝑥−20° 𝑧 4𝑥+60° C E 1 (a) Josh assumes that BC and DE are parallel. What answer should she get for the size of angle 𝑧? [4 marks] 8𝑥−20=4𝑥+60 4𝑥+60= 4𝑥−20=60 4 20 +60=140 4𝑥=80 𝑥=20 180 −140=40 40 Answer degrees 1 (b) In fact, AB and CD are not parallel angle 𝑤 is 130° What effect does this have on the size of angle 𝑧? Tick a box. 𝑧 is bigger 𝑧 is the same 𝑧 is smaller Show working to support your answer. [3 marks] 8𝑥−20 = 140 4𝑥+60° must be smaller 140>130 𝑤 𝑧 must be bigger 𝑥 must be smaller

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