In the given figure find the value of $∠ A O C$ .

130^{\circ}

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140^{\circ}

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150^{\circ}

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160^{\circ}

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Solution

The correct option is B $140^{\circ}$
$I n t h e a b o v e f i g u r e ∠ B A O = 30 a n d ∠ B C O = 40...... (1) O A, O B a n d O C a r e d i a m e t e r o f c i r c l e H e n c e O A = O B = O C T h e a n g l e s o p p o s i t e t o t h e e q u a l s i d e s a r e e q u a l \Rightarrow ∠ B A O = ∠ A B O S i m i l a r l y ∠ B C O = ∠ C B O \Rightarrow ∠ A B O = 30 a n d ∠ C B O = 40 [F r o m (1)] N o w ∠ A B C = ∠ A B O + ∠ C B O \Rightarrow ∠ A B C = 30 + 40 = 70......... (2) ∠ A O C = 2 ∠ A B C = 2 \times 70 = 140 [F r o m (2)] H e n c e o p t i o n B i s r i g h t a n s w e r$

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Similar questions

Find the value of $∠$ COB.

∠ A O C

∠ B O C

a - 2 b = 30^{\circ}

154

Classes	$120 - 130$	$130 - 140$	$140 - 150$	$150 - 160$	$160 - 170$	$170 - 180$
Frequency	$2$	$8$	$12$	$f$	$8$	$7$

\begin{matrix} H e i g h t (i n c m) & 100 - 110 & 110 - 120 & 120 - 130 & 130 - 140 & 140 - 150 & 150 - 160 & 160 - 170 & 170 - 180 N o . o f g o a l s s c o r e d & 8 & 10 & 15 & 9 & 12 & 14 & 13 & 10 \end{matrix}

In the given figure, if $∠ A O C = 130^{\circ},$ find the value of $∠ A B C$ .

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