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
[tex]x^\circ+53^\circ=164^\circ[/tex]
[tex]x^\circ=164^\circ-53^\circ[/tex]
[tex]x^\circ=111^\circ[/tex]
[tex]x=111[/tex]
Therefore, the value of x is 111.
