Question

An exterior angle of a triangle is equal to the sum of two ______ .

• A. interior angles
• B. adjacent interior angles
• C. opposite exterior angles
• D. opposite interior angles

Answer 1

The correct option is D opposite interior angles

An exterior angle of a triangle is equal to the sum of two opposite interior angles.

Consider the given triangle, we can easily apply the exterior angle property of triangle.

For the given triangle XYZ, we have

$\angle 1+\angle 2+\angle XYZ={180}^{\circ }$ [Angle sum property of triangle]

$\angle 1+\angle 2={180}^{\circ }-\angle XYZ\dots \dots \left(i\right)$

$\angle XYZ+\angle 3={180}^{\circ }$ [Linear pair]

$\angle 3={180}^{\circ }-\angle XYZ\dots \dots \left(ii\right)$

From $eq.\left(i\right)$ and $\left(ii\right),$ we can say

$\angle 1+\angle 2=\angle 3$

Here, $\angle 1$ and $\angle 2$ are opposite interior angles.

and, $\angle 3$ is an exterior angle.

Hence, An exterior angle of a triangle is equal to the sum of two opposite interior angles.