Question

10)given the two parallel lines cute by a transversal, what is the measure of ∠5?

Explanation:

Step1: Find the measure of adjacent angle

Since the angle of $85^{\circ}$ and $\angle8$ are vertical angles, $\angle8 = 85^{\circ}$. And $\angle5$ and $\angle8$ are supplementary angles (they form a linear - pair).

Step2: Calculate the measure of $\angle5$

Using the supplementary - angle formula $\angle5+\angle8 = 180^{\circ}$. Substitute $\angle8 = 85^{\circ}$ into the formula: $\angle5=180^{\circ}-\angle8$. So, $\angle5 = 180^{\circ}-85^{\circ}=95^{\circ}$.

Answer:

$95^{\circ}$