In the give figure, and are two intersecting chords of a circle. If ∠CAB = 40° and ∠BCD = 80°, then ∠CBD = ?

Question

In the give figure, and are two intersecting chords of a circle. If ∠ CAB = 40° and ∠ BCD = 80°, then ∠ CBD = ?

Philoid · Accepted Answer

Given: and ∠BCD = 80°

Here,

∠CAB = ∠CDB = 40° ( angles in the same segment drawn from same chord are equal).

Now, in ΔBCD

By angle sum property

∠BCD + ∠CDB + ∠CBD = 180°

80° + 40° + ∠CBD = 180°

∠CBD = 180° – 40° – 80°

∠CBD = 60°

∴ ∠CBD = 60°