Question

in the figure below, m∠3 = 33°. find m∠1, m∠2, and 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 $m\angle1$

Since $\angle1$ and $\angle3$ are vertical angles, $m\angle1 = m\angle3=33^{\circ}$.

Step3: Find $m\angle2$

$\angle2$ and $\angle3$ are supplementary (form a straight - line pair), so $m\angle2=180^{\circ}-m\angle3$. Substituting $m\angle3 = 33^{\circ}$, we get $m\angle2 = 180 - 33=147^{\circ}$.

Step4: Find $m\angle4$

Since $\angle4$ and $\angle2$ are vertical angles, $m\angle4 = m\angle2 = 147^{\circ}$.

Answer:

$m\angle1 = 33^{\circ}$, $m\angle2 = 147^{\circ}$, $m\angle4 = 147^{\circ}$