In the given figure, find the value of $^{'} a^{'}$ is

170^{\circ}

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20^{\circ}

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10^{\circ}

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5^{\circ}

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Solution

The correct option is D $5^{\circ}$
$∠ A B P = 85 (G i v e n) ∠ A O B = 2 (∠ A B P) (A n g l e i n c r i b e d b y c e n t r e o f c i r c l e i s d o u b l e a n g l e i n s c r i b e d b y a n y c h o r d) ∠ A O B = 2 \times 85 = 170 I n △ A O B S i n c e O A = O B (O i s c e n t r e o f c i r c l e) ∠ O A B = ∠ O B A (A n g l e a l o n g t h e e q u a l s i d e a r e e q u a l) H e n c e ∠ O A B + ∠ O B A + ∠ A O B = 180 ∠ O A B + ∠ O B A = 180 - 170 = 10 H e n c e ∠ O A B = ∠ O B A = 5 ∠ O A B = a = 5 H e n c e o p t i o n (D) i s t h e c o r r e c t a n s w e r$

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