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Alternate Exterior Angles

In the figure...

Question

$In the figure given, AOB is a straight line. What is$
$the value of a$ .

15^{\circ}

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12^{\circ}

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60^{\circ}

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20^{\circ}

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Solution

The correct option is A $15^{\circ}$

Given,

AOB is a straight line

In the given figure,
$∠ A O C + ∠ C O D + ∠ D O E + ∠ E O B = 180^{\circ} [Angles on a straight line]$

$⟹ 35^{\circ} + 45^{\circ} + 4 a^{\circ} + 40^{\circ} = 180^{\circ}$

$⟹ 4 a + 120^{\circ} = 180^{\circ}$

$⟹ 4 a = 180^{\circ} - 120^{\circ}$

$⟹ 4 a = 60^{\circ}$

$⟹ a = 15^{\circ}$

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