Question

a side of the triangle below has been extended to form an exterior angle of 127°. find the value of x.
find all the measure of the missing angles in the triangle below.

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 $127^{\circ}$. So we have the equation $x + 90^{\circ}=127^{\circ}$.

Step2: Solve for $x$

Subtract $90^{\circ}$ from both sides of the equation: $x=127^{\circ}-90^{\circ}$.
$x = 37^{\circ}$

Answer:

$37^{\circ}$