Question

in the figure below, m∠1 = 102°. 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. Also, $\angle1$ and $\angle2$ are supplementary (linear - pair).

Step2: Find $m\angle2$

Since $\angle1$ and $\angle2$ form a linear - pair, $m\angle1 + m\angle2=180^{\circ}$. Given $m\angle1 = 102^{\circ}$, then $m\angle2=180^{\circ}-102^{\circ}=78^{\circ}$.

Step3: Find $m\angle3$

Because $\angle1$ and $\angle3$ are vertical angles, $m\angle3 = m\angle1=102^{\circ}$.

Step4: Find $m\angle4$

Since $\angle2$ and $\angle4$ are vertical angles, $m\angle4 = m\angle2=78^{\circ}$.

Answer:

$m\angle2 = 78^{\circ}$, $m\angle3 = 102^{\circ}$, $m\angle4 = 78^{\circ}$