Question

a side of the triangle below has been extended to form an exterior angle of 131°. 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 $180^\circ - 131^\circ = 49^\circ$.

Step2: Use the triangle angle sum property

The triangle is a right triangle, so the sum of the two non - right angles is $90^\circ$. Let the unknown angle be $x$. We know one non - right angle is $49^\circ$, so $x+49^\circ = 90^\circ$. Then $x=90^\circ - 49^\circ = 41^\circ$.

Answer:

$x = 41$