From the figure given below, find out the measure of ∠COB and ∠AOC respe

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From the figure given below, find out the measure of $∠$ COB and $∠$ AOC respectively.

Options:

A . 24

^{\circ}

and 126

^{\circ}

B . 42

^{\circ}

and 156

^{\circ}

C . 24

^{\circ}

and 156

^{\circ}

D . 42

^{\circ}

and 126

^{\circ}

Answer: Option C
:
C

Since AB is a straight line, $∠ A O B = 180^{\circ}$

Therefore, $∠ A O C + ∠ C O B = 180^{\circ}$

$\Rightarrow 3 x + 30^{\circ} + 2 x - 60^{\circ} = 180^{\circ}$

$\Rightarrow 5 x - 30^{\circ} = 180^{\circ}$

$\Rightarrow 5 x = 210^{\circ}$

$\Rightarrow x = 42^{\circ}$

Therefore,

$∠ C O B = 2 x - 60^{\circ} = 84^{\circ} - 60^{\circ} = 24^{\circ}$

$∠ A O C = 3 x + 30^{\circ} = 126^{\circ} + 30^{\circ} = 156^{\circ}$

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