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 $95^{\circ}$ 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 $95^{\circ}+x = 180^{\circ}$.
Solve for $x$: $x=180^{\circ}-95^{\circ}=85^{\circ}$. So, $m\angle4 = 85^{\circ}$.

Answer:

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