Question

a side of the triangle below has been extended to form an exterior angle of 112°. find the value of x.

Explanation:

Step1: Recall exterior - angle property

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In this right - triangle, one non - adjacent interior angle is $x$ and the other is $90^{\circ}$, and the exterior angle is $112^{\circ}$. So, $x + 90^{\circ}=112^{\circ}$.

Step2: Solve for $x$

Subtract $90^{\circ}$ from both sides of the equation: $x=112^{\circ}-90^{\circ}$.

Answer:

$22$