Question

a side of the triangle below has been extended to form an exterior angle of 164°. find the value of x.
(there is a triangle with an exterior angle of 164° and an interior angle of 112° and another interior angle 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 the triangle angle sum property

The sum of the interior angles of a triangle is $180^\circ$. Let the three angles be $16^\circ$, $112^\circ$, and $x^\circ$. So we have the equation $16^\circ + 112^\circ + x^\circ = 180^\circ$.

Step3: Solve for x

First, calculate $16^\circ + 112^\circ = 128^\circ$. Then, $x^\circ = 180^\circ - 128^\circ = 52^\circ$.

Answer:

$x = 52$