Question

what is the value of z? a 88 b 92 c 95 d 124

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle opposite to the $95^{\circ}$ angle is also $95^{\circ}$.

Step2: Consider linear - pair property

A linear - pair of angles sums to $180^{\circ}$. We know that $z + 88^{\circ}=180^{\circ}$ (by finding the adjacent angle to the $92^{\circ}$ angle formed in the figure). First, we find the angle inside the triangle adjacent to the $95^{\circ}$ angle. The sum of angles in a triangle is $180^{\circ}$. In the triangle with angles $42^{\circ}$, $53^{\circ}$, and the third angle, the third angle is $180-(42 + 53)=85^{\circ}$. Then, using linear - pair and angle - addition properties, we find that the angle adjacent to $z$ is $88^{\circ}$.
So, $z=180 - 88=92^{\circ}$

Answer:

B. 92