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

Question:

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

(b) 60°
(c) 50°
(d) 70°

Figure

Solution:

(b) 60°
We have:
∠CDB = ∠CAB = 40°  (Angles in the same segment of a circle)
In Δ CBD, we have:
∠CDB + ∠BCD +∠CBD = 180°   (Angle sum property of a triangle)
⇒ 40° + 80° + ∠CBD = 180°
⇒ ∠CBD = (180° - 120°) = 60°

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