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Exterior Angle of a Triangle and Its Property

Question

Find the value of exterior angle.

$100^{\circ}$
$110^{\circ}$
$120^{\circ}$
$115^{\circ}$

A

110^{\circ}

B

115^{\circ}

C

100^{\circ}

D

120^{\circ}

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Solution

Verified by Toppr

An exterior angle of a triangle is equal to the sum of the opposite interior angles.
So by this property:
$x - 20^{\circ} + 2 x - 45^{\circ} = 2 x - 5^{\circ}$
$3 x - 65^{\circ} = 2 x - 5^{\circ}$
$3 x - 2 x = 65^{\circ} - 5^{\circ}$
$x = 60^{\circ}$
Therefore, $∠$ $F$ exterior angle $= 2 x - 5^{\circ}$
$= 2 \times 60^{\circ} - 5^{\circ} = 115^{\circ}$

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