If O is the centre of the given circle, such that ∠AOC = 110° and side AB is produced to D, find ∠CBD.

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Solution

$Major ∠ A O C = 360 ° - 110 ° = 250 ° (complete angle) We know that the angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle . So, ∠ C B A = \frac{1}{2} Major ∠ A O C \Rightarrow ∠ C B A = \frac{1}{2} \times 250 ° \Rightarrow ∠ C B A = 125 ° Now, ∠ C B A + ∠ C B D = 180 ° (Linear pair) \Rightarrow ∠ C B D = 180 ° - ∠ C B A \Rightarrow ∠ C B A = 180 ° - 125 ° \Rightarrow ∠ C B A = 55 °$

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Similar questions

∠ A O C = 100^{o}

∠ C B D

∠ A B C

In the given figure, O is centre of a circle in which $∠ A O C = 100^{\circ}$ . Side AB of quad. OABC has been produced to D. Then, $∠$ CBD = ?

(a) $50^{\circ}$

(b) $40^{\circ}$

(d) $80^{\circ}$

∠

= 110^{o}

∠

B A

△ A B C

D

C D = C A

C B

E

∠ B A C = 106^{0}

∠ A B E = 128^{0}

∠ B C D

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