Question

angles and transformations
finding angle measures given two intersecting lines
in the figure below, m∠3 = 107°. find m∠1, m∠2, and m∠4.

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles.
$m\angle1 = m\angle3$

Step2: Determine the measure of $\angle1$

Since $m\angle3 = 107^{\circ}$, then $m\angle1=107^{\circ}$

Step3: Identify linear - pair angles

$\angle2$ and $\angle3$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. So $m\angle2 + m\angle3=180^{\circ}$

Step4: Calculate the measure of $\angle2$

$m\angle2=180^{\circ}-m\angle3 = 180 - 107=73^{\circ}$

Step5: Identify vertical - angles again

$\angle2$ and $\angle4$ are vertical angles. So $m\angle4 = m\angle2$

Step6: Determine the measure of $\angle4$

$m\angle4 = 73^{\circ}$

Answer:

$m\angle1 = 107^{\circ}$
$m\angle2 = 73^{\circ}$
$m\angle4 = 73^{\circ}$