UniGeniusGCSE Maths · Edexcel 1MA1

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Circle theorems and angle chains

3 exam-style questions. Answers and the mark for each step are on the last page.

  1. Question 1Non-calculator · 3 marks

    (a) ABCD is a cyclic quadrilateral, with its vertices in that order around the circle. Angle BAD is (3x + 14)∘^\circ and angle BCD is (5x + 6)∘.^\circ. Work out angle BAD. (3)

  2. Question 2Non-calculator · 3 marks

    (a) A, B, C and D lie in that order on a circle. AB = AD. Angle ABD is (3x −- 4)∘^\circ and angle BCD is (4x + 18)∘.^\circ. Work out angle BAD. You must show your working. (3)

  3. Question 3Non-calculator · 4 marks

    A, B, C and D are consecutive vertices of a cyclic quadrilateral. Angle BCD is 100∘100^\circ. AB = AD.

    (a) Find angle BAD. (2)

    (b) Find angle ABD. (2)

Answers and marks

Question 1

(a) 7474°

  • P1 Establishing 3x+14+5x+6=1803x+14+5x+6=180 or an equivalent valid method.
  • P1 Establishing 8x=1608x=160 or an equivalent valid method.
  • A1 Correct answer: 7474°

Question 2

(a) 110110°

  • P1 Establishing 180−2(3x−4)+4x+18=180180-2(3x-4)+4x+18=180 or an equivalent valid method.
  • P1 Establishing x=13x=13 or an equivalent valid method.
  • A1 Correct answer: 110110°

Question 3

(a) 8080°

  • M1 Opposite angles in a cyclic quadrilateral sum to 180 degrees.
  • A1 Correct answer: 8080°

(b) 5050°

  • M1 AB=AD makes triangle ABD isosceles.
  • A1 Correct answer: 5050°

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Circle theorems and angle chains

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