Question

Prove that the measure of the exterior angle of a triangle is equal to the sum of the two remote angles?

Answer 1

As proved below.

Explanation:

For a given triangle, sum of the three angles = `180^0`
As per the diagram, `angle1 +angle 2 +angle 3 = 180^0`

AD is a straight line and CB stands on it.
Therefore, angle 2 and angle 4 are supplementary.
I.e. `angle 2 + angle 4 = 180^0`

Hence `angle 1 + cancel(angle 2) + angle 3 = cancel (angle 2) + angle 4`

`:. angle 1 + angle 3 = angle 4`

In other words, exterior angle is equal to sum of the two interior opposite (remote) angles.

Similarly, we can prove the other 5 exterior angles