Question

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

the value of x.
1649

Answer 1

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

`x^\circ+53^\circ=164^\circ`

`x^\circ=164^\circ-53^\circ`

`x^\circ=111^\circ`

`x=111`

Therefore, the value of x is 111.