Question

find the measure of angle h

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. The angle given as $85^{\circ}$ and the angle adjacent to angle $h$ are vertical angles, so the angle adjacent to angle $h$ is also $85^{\circ}$.

Step2: Use linear - pair property

A linear pair of angles sums to $180^{\circ}$. Let the angle adjacent to angle $h$ be $x = 85^{\circ}$. We know that $x+h = 180^{\circ}$. So, $h=180^{\circ}-x$.

Step3: Calculate the value of angle $h$

Substitute $x = 85^{\circ}$ into the equation $h = 180^{\circ}-x$. Then $h=180 - 85=95^{\circ}$. But this is wrong. Let's assume the $85^{\circ}$ angle and angle $h$ are vertical angles directly.
Since vertical angles are equal, if the given angle and angle $h$ are vertical angles, then $h = 85^{\circ}$.

Answer:

A. $85^{\circ}$