Question

lines e and f are parallel. the m∠9 = 80° and m∠5 = 55°. which angle measures are correct? select three options. m∠2 = 125° m∠3 = 55° m∠8 = 55° m∠12 = 100° m∠14 = 100°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle5$ and $\angle3$ are vertical angles. Since $m\angle5 = 55^{\circ}$, then $m\angle3=55^{\circ}$.

Step2: Use corresponding - angle property

$\angle5$ and $\angle8$ are corresponding angles. Corresponding angles formed by parallel lines are equal. Since $m\angle5 = 55^{\circ}$, then $m\angle8 = 55^{\circ}$.

Step3: Use linear - pair and corresponding - angle property

$\angle9$ and $\angle11$ are vertical angles, so $m\angle11 = 80^{\circ}$. $\angle11$ and $\angle14$ are corresponding angles, so $m\angle14=80^{\circ}$. $\angle9$ and $\angle12$ are a linear - pair. Since $\angle9 = 80^{\circ}$, then $m\angle12=180 - 80=100^{\circ}$.

Answer:

B. $m\angle3 = 55^{\circ}$
C. $m\angle8 = 55^{\circ}$
D. $m\angle12 = 100^{\circ}$