Question

in the figure below, m∠1 = 96°. find m∠2, m∠3, and m∠4.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles. So $m\angle3=m\angle1 = 96^{\circ}$.

Step2: Use linear - pair property

$\angle1$ and $\angle2$ form a linear pair. Since the sum of angles in a linear pair is $180^{\circ}$, we have $m\angle2=180^{\circ}-m\angle1$. Substituting $m\angle1 = 96^{\circ}$, we get $m\angle2=180 - 96=84^{\circ}$.

Step3: Use vertical - angle property again

$\angle2$ and $\angle4$ are vertical angles. So $m\angle4=m\angle2 = 84^{\circ}$.

Answer:

$m\angle2 = 84^{\circ}$, $m\angle3 = 96^{\circ}$, $m\angle4 = 84^{\circ}$