Question

in the diagram, m∠3 = 120° and m∠12 = 80°. which angle measures are correct? check all that apply. m∠1 = 60° m∠13 = 80° m∠6 = 80° m∠5 = 60° m∠10 = 120° m∠14 = 100°

Explanation:

Step1: Use linear - pair property

$\angle1$ and $\angle3$ form a linear - pair. Since $m\angle3 = 120^{\circ}$, and the sum of angles in a linear - pair is $180^{\circ}$, then $m\angle1=180 - 120=60^{\circ}$.

Step2: Use vertical - angle property

$\angle12$ and $\angle13$ are vertical angles. Vertical angles are equal. So $m\angle13 = m\angle12=80^{\circ}$.

Step3: Use corresponding - angle property

$\angle12$ and $\angle6$ are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. So $m\angle6 = m\angle12 = 80^{\circ}$.

Step4: Use linear - pair property for $\angle5$

$\angle5$ and $\angle3$ are corresponding angles. Since $\angle3 = 120^{\circ}$, and $\angle5$ and $\angle3$ are corresponding angles, $m\angle5=180 - 120 = 60^{\circ}$ (using the linear - pair property related to the parallel - line setup).

Step5: Use linear - pair property for $\angle10$

$\angle10$ and $\angle12$ form a linear - pair. So $m\angle10=180 - 80 = 100^{\circ}$, not $120^{\circ}$.

Step6: Use linear - pair property for $\angle14$

$\angle14$ and $\angle12$ form a linear - pair. So $m\angle14=180 - 80 = 100^{\circ}$.

Answer:

$m\angle1 = 60^{\circ}$, $m\angle13 = 80^{\circ}$, $m\angle6 = 80^{\circ}$, $m\angle5 = 60^{\circ}$, $m\angle14 = 100^{\circ}$