Question

a side of the triangle below has been extended to form an exterior angle of 164°. find the value of x.

Explanation:

Step1: Find the adjacent interior angle

The exterior angle and its adjacent interior angle are supplementary, so the adjacent interior angle is $180^\circ - 164^\circ = 16^\circ$.

Step2: Use triangle angle sum

The sum of angles in a triangle is $180^\circ$. So $x + 112^\circ + 16^\circ = 180^\circ$.

Step3: Solve for x

$x = 180^\circ - 112^\circ - 16^\circ = 52^\circ$.

Answer:

$52^\circ$