lines e and f are parallel. the m∠9 = 80° and m∠5 = 55°. which angle measures are correct? select three…

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 linear - pair property

$\angle9$ and $\angle12$ are a linear - pair. A linear - pair of angles is supplementary, so $m\angle9 + m\angle12=180^{\circ}$. Given $m\angle9 = 80^{\circ}$, then $m\angle12=180 - 80=100^{\circ}$.

Step3: Use corresponding - angle property

$\angle5$ and $\angle8$ are corresponding angles. Since lines $e$ and $f$ are parallel, corresponding angles are equal. So $m\angle8 = m\angle5=55^{\circ}$.

Answer:

$m\angle3 = 55^{\circ}$, $m\angle8 = 55^{\circ}$, $m\angle12 = 100^{\circ}$