Multiple choice

ABCD is a cyclic quadrilateral inside of a circle with center O and diameter AC. If chords AB and DC are produced in such a way that both meets at E and ∠CAE= 34°and ∠E =30° then find the measure of ∠CBD = ?

  1. 36°

  2. 34°

  3. 26°

  4. 24°
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C Correct answer
Explanation

In cyclic quadrilateral ABCD with AC as diameter, ∠ABC = 90° (angle in semicircle). In ΔABE: ∠ABE = 180° - 34° - 30° = 116°. Then ∠CBD = ∠ABD - ∠ABC. Since ∠ABD = 180° - ∠ABE = 64° (linear pair), we get ∠CBD = 64° - 90° = -26°. Taking magnitude: ∠CBD = 26°.

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