Question

See the image for diagram and please help me. Question: The measure of an exterior angle of a triangle is equal to the sum of its remote interior angles.​

Answer 1

Step-by-step explanation:

Here, $\angle \:$PRS is the exterior angle of the triangle. And the remote interior angle is $\angle$PRQ.

The $\angle$PRQ when doubled equals $\angle$ PRS.

$\angle$ PRQ×2 = $\angle$PRS

Hence, we can say that the measure of an exterior angle of a triangle is equal to the sum of its opposite or remote interior angles.

Hope it helps

Answer 2

Answer:

Remember that the two non-adjacent interior angles opposite the exterior angle are sometimes referred to as remote interior angles. An exterior angle of a triangle is equal to the sum of the two opposite interior angles. The sum of exterior angle and interior angle 180 degrees

STEP to STEP EXPLANATION

For a given triangle , sum of interior angles is 180 degree

So angle P + angle Q + angle R(interior) = 180 degree

QS is a straight line and PR stands on it

So angle R(interior) + angle R(exterior) are supplementary angles

Therefore , angle R(interior) + angle R(exterior)  =  180 degree

Hence angleP + angleQ + angleR(interior) = angle R(interior) + angle R(ext)

So , angle P + angle Q = angle R(exterior)

HENCE  ,  PROVED