Question

find the value of x.

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). First, find the third interior angle.
Let the third interior angle be \(y\). So, \(52^\circ + 79^\circ + y = 180^\circ\).
Calculating \(y\): \(y = 180^\circ - 52^\circ - 79^\circ = 49^\circ\).

Step2: Use linear pair (supplementary angles)

The angle \(x\) and \(y\) form a linear pair, so they are supplementary (sum to \(180^\circ\)).
Thus, \(x + y = 180^\circ\). Substituting \(y = 49^\circ\), we get \(x = 180^\circ - 49^\circ = 131^\circ\).

Answer:

\(131^\circ\)