Question

1. find the measures of the numbered angles. measure of ∠3: measure of ∠4:

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle3$ and the given $95^{\circ}$ angle are vertical angles.
So, $m\angle3 = 95^{\circ}$

Step2: Identify linear - pair relationship

$\angle3$ and $\angle4$ form a linear pair. The sum of angles in a linear pair is $180^{\circ}$.
Let $m\angle4=x$. Then $m\angle3 + x=180^{\circ}$. Since $m\angle3 = 95^{\circ}$, we have $x = 180^{\circ}-95^{\circ}=85^{\circ}$

Answer:

measure of $\angle3$: $95^{\circ}$
measure of $\angle4$: $85^{\circ}$