Question

in the figure below, the measure of ∠4 = 90°, the measure of ∠5 = 65°, and the measure of ∠6 = 25°. 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. Since $m\angle4 = 90^{\circ}$, then $m\angle1=90^{\circ}$. $\angle2$ and $\angle6$ are vertical angles.

Step2: Find measure of $\angle2$

Since $\angle2$ and $\angle6$ are vertical angles, and $m\angle6 = 25^{\circ}$, then $m\angle2=25^{\circ}$.

Step3: Find measure of $\angle3$

$\angle3$ and $\angle5$ are vertical angles. Since $m\angle5 = 65^{\circ}$, then $m\angle3 = 65^{\circ}$.

Answer:

$m\angle2 = 25^{\circ}$, $m\angle3=65^{\circ}$