Question

in the figure below, m∠1 = 107°. find m∠2, m∠3, and m∠4. m∠2 = m∠3 = m∠4 =

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles, and $\angle2$ and $\angle4$ are vertical angles.

Step2: Find $\angle3$

Since $\angle1$ and $\angle3$ are vertical angles, $m\angle3=m\angle1 = 107^{\circ}$.

Step3: Use linear - pair relationship

$\angle1$ and $\angle2$ form a linear pair. The sum of angles in a linear pair is $180^{\circ}$. So $m\angle2=180 - m\angle1$.
$m\angle2=180 - 107=73^{\circ}$.

Step4: Find $\angle4$

Since $\angle2$ and $\angle4$ are vertical angles, $m\angle4=m\angle2 = 73^{\circ}$.

Answer:

$m\angle2 = 73^{\circ}$, $m\angle3 = 107^{\circ}$, $m\angle4 = 73^{\circ}$