Question

in the figure below, the measure of ∠4 = 90°, the measure of ∠5 = 56°, and the measure of ∠6 = 34°. what are the measures of ∠1, ∠2 and ∠3? m∠1 = 90° m∠2 =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle4$ are vertical angles. Given $\angle4 = 90^{\circ}$, so $\angle1=90^{\circ}$.

Step2: Use angle - sum property of a straight - line

$\angle2+\angle3+\angle4 = 180^{\circ}$ (since they form a straight - line). Also, $\angle3$ and $\angle5$ are vertical angles, so $\angle3=\angle5 = 56^{\circ}$. Then $\angle2=180^{\circ}-\angle3 - \angle4$.
Substitute $\angle3 = 56^{\circ}$ and $\angle4 = 90^{\circ}$ into the formula: $\angle2=180^{\circ}-56^{\circ}-90^{\circ}=34^{\circ}$.

Answer:

$m\angle1 = 90^{\circ}$, $m\angle2 = 34^{\circ}$