Question 2

Explanation

From the figure, we can see that the angle vertically opposite to $z^\circ$ is the angle between the two diagonal lines at the top. The measure of that angle is equal to $z^\circ$.

Since the angles on a straight line sum to $180^\circ$, the sum of angle $x^\circ$, vertical angle $z^\circ$, and $y^\circ$ is $180^\circ$:

Given that $x^\circ = y^\circ$, we can substitute $y$ with $x$:

Therefore, the measure of angle $z$ is $180 - 2x$.