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 = □°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle5$ are vertical angles.

Step2: Determine $\angle1$ measure

Since vertical angles are equal and $m\angle5 = 56^{\circ}$, then $m\angle1=56^{\circ}$.

Step3: Determine $\angle2$ measure

$\angle2$ and $\angle6$ are vertical angles. So $m\angle2 = 34^{\circ}$ because vertical angles are equal.

Step4: Determine $\angle3$ measure

$\angle3$ and $\angle4$ are vertical angles. So $m\angle3 = 90^{\circ}$ because vertical angles are equal.

Answer:

$m\angle1 = 56^{\circ}$, $m\angle2=34^{\circ}$, $m\angle3 = 90^{\circ}$