Question

fill in the blank 4 points if ∠1 and ∠2 are congruent and supplementary angles, how much does each angle measure? m∠1 = type your answer... degrees m∠2 = type your answer...

Explanation:

Step1: Recall angle - relationship definitions

Congruent angles have equal measures, i.e., $m\angle1=m\angle2$. Supplementary angles add up to 180 degrees, so $m\angle1 + m\angle2=180^{\circ}$.

Step2: Substitute and solve

Since $m\angle1=m\angle2$, substitute $m\angle2$ for $m\angle1$ in $m\angle1 + m\angle2=180^{\circ}$. We get $m\angle2+m\angle2 = 180^{\circ}$, or $2m\angle2=180^{\circ}$. Then $m\angle2=\frac{180^{\circ}}{2}=90^{\circ}$. And since $m\angle1=m\angle2$, $m\angle1 = 90^{\circ}$ too.

Answer:

$m\angle1 = 90$
$m\angle2 = 90$