A side of the triangle below has been extended to form an exterior angle of 164". Find the value of x.
1649

Given:

Measure of exterior angle = 164°

The measure of opposite interior angles are x° and 53°.

To find:

The value of x.

Solution:

According to the Exterior Angle Theorem, in a triangle the measure of an exterior angles is always equal to the sum of measures of two opposite interior angles.

Using Exterior Angle Theorem, we get

Therefore, the value of x is 111.