Question

the diagram shows parallel lines a and b cut by transversals c and d. m∠5 = 85°. m∠3 = 115°. what are the measures of ∠2, ∠12, and ∠16? use the drop - down menus to identify each angle measure.

Explanation:

Step1: Use vertical - angle property

$\angle3$ and $\angle2$ are vertical angles. Vertical angles are congruent. Given $m\angle3 = 115^{\circ}$, so $m\angle2=115^{\circ}$.

Step2: Use corresponding - angle property

$\angle5$ and $\angle12$ are corresponding angles. Corresponding angles formed by parallel lines and a transversal are congruent. Given $m\angle5 = 85^{\circ}$, so $m\angle12 = 85^{\circ}$.

Step3: Use vertical - angle property

$\angle3$ and $\angle16$ are vertical angles. Since vertical angles are congruent and $m\angle3 = 115^{\circ}$, so $m\angle16=115^{\circ}$.

Answer:

$m\angle2 = 115^{\circ}$, $m\angle12 = 85^{\circ}$, $m\angle16 = 115^{\circ}$