2019Q11(c)(ii)Circles

NumericalEasy1 mark

11(c)

In the given figure, ABCDE is a pentagon inscribed in a circle such that AC is a diameter and side BC||AE. If ∠BAC = 50°, find giving reasons:

Figure for this question

∠EDC

Topic: Circle theorems

Previous-year question practice database

Answer

Exam answer

AE ∥ BC.

∠EAC = ∠ACB = 40°.

In cyclic quadrilateral ACDE: ∠EAC + ∠EDC = 180°.

∠EDC = 140°.

Answer: 140°.

Explanation

Use parallel-line angles, then opposite angles of a cyclic quadrilateral.

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