Cyclic Quadrilaterals — O/L Mathematics

How do I practise Cyclic Quadrilaterals?

1 question with a worked solution

1. In a cyclic quadrilateral ABCD, the opposite angles satisfy angle A = 3x and angle C = 2x + 20°. Find the magnitude of angle A.
   1. A) 96°
   2. B) 100°
   3. C) 32°
   4. D) 84°
   Check my answer

   Correct answer: A) 96°

   Opposite angles of a cyclic quadrilateral are supplementary: angle A + angle C = 180° → 3x + (2x + 20°) = 180° → 5x = 160° → x = 32°. Therefore, angle A = 3(32°) = 96°.

   Show worked solution

   Step 1: State cyclic quadrilateral theorem: Opposite angles sum to 180°. Step 2: Set up equation: 3x + 2x + 20° = 180°. Step 3: 5x = 160° → x = 32°. Step 4: Calculate angle A: angle A = 3x = 3 × 32° = 96°. Answer: 96°.
   Modelled on: the O/L Mathematics examination pattern

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Where does Cyclic Quadrilaterals fit in the syllabus?

Grade 11 · Term 3