Question

consider the figure. enter the measure of angle z, in degrees, in the space provided.

Explanation:

Step1: Recall exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. Let the non - adjacent interior angles of the exterior angle of measure $142^{\circ}$ be $x$ and $90^{\circ}$.

Step2: Set up the equation

We have the equation $142^{\circ}=x + 90^{\circ}$.

Step3: Solve for $x$

Subtract $90^{\circ}$ from both sides of the equation: $x=142^{\circ}-90^{\circ}=52^{\circ}$.

Answer:

$52$