In the given figure, AB and CD are two intersecting chords of a circle. If $∠ C A B = 40^{\circ} a n d ∠ B C D = 80^{\circ} then ∠ C B D = ?$

(a) $80^{\circ}$

(b) $60^{\circ}$

(c) $50^{\circ}$

(d) $70^{\circ}$

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Solution

ANSWER:
( 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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Similar questions

Q. 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

Q. In ∆ABC, BD ⊥ AC, ∠CAE = 30° and ∠CBD = 40°. Then, ∠AEB = ?
(a) 70°
(b) 80°
(c) 50°
(d) 60°

$A B C D$ is a cyclic quadrilateral whose diagonals intersect at a point $E$ . If $∠ D B C = 70^{\circ}$ and $∠ B A C = 30^{\circ}$ , then $∠ B C D$ = ___. Further, if $A B = B C$ , then $∠ E C D$ = ___.

Q. If PA and PB are two tangents to a circle with centre O, such that ∠APB = 80°, then ∠AOP = ?

(a) 40°
(b) 50°
(c) 60°
(d) 70°

In $Δ A B C$ If $∠ B = ∠ C$ and $∠ A = 80^{\circ},$ then $∠ C =$ ___.

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In the given 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∘

ANSWER: ( 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°

In the given figure, AB and CD are two intersecting chords of a circle. If $∠ C A B = 40^{\circ} a n d ∠ B C D = 80^{\circ} then ∠ C B D = ?$

(a) $80^{\circ}$

(b) $60^{\circ}$

(c) $50^{\circ}$

(d) $70^{\circ}$

ANSWER:
( 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°