Question

in the figure below, the measure of ∠4 = 50°, the measure of ∠5 = 61°, and the measure of ∠6 = 29°. what are the measures of ∠1, ∠2, and ∠3?

m∠1 = □°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Assume that $\angle 4$ and $\angle 1$ are vertical angles, $\angle 5$ and $\angle 2$ are vertical angles, $\angle 6$ and $\angle 3$ are vertical angles.

Step2: Find measure of $\angle 1$

Since vertical angles are equal and $\angle 4 = 50^{\circ}$, then $m\angle 1=50^{\circ}$.

Step3: Find measure of $\angle 2$

Since vertical angles are equal and $\angle 5 = 61^{\circ}$, then $m\angle 2 = 61^{\circ}$.

Step4: Find measure of $\angle 3$

Since vertical angles are equal and $\angle 6 = 29^{\circ}$, then $m\angle 3=29^{\circ}$.

Answer:

$m\angle 1 = 50^{\circ}$, $m\angle 2 = 61^{\circ}$, $m\angle 3 = 29^{\circ}$