Question

part 1 of 3
if m || n and m∠e = 92° in the figure to the right, find the measures of ∠a, ∠c, and ∠h.
m∠a = □° (type an integer or a decimal)

Explanation:

Step1: Identify angle - pair relationship

$\angle a$ and $\angle e$ are vertical angles.

Step2: Use vertical - angle property

Vertical angles are congruent. Since $m\angle e = 92^{\circ}$, then $m\angle a=m\angle e$.

Step3: Find $\angle c$

$\angle c$ and $\angle e$ are corresponding angles. Corresponding angles are congruent when $m\parallel n$. So $m\angle c = m\angle e=92^{\circ}$.

Step4: Find $\angle h$

$\angle h$ and $\angle e$ are alternate - exterior angles. Alternate - exterior angles are congruent when $m\parallel n$. So $m\angle h=m\angle e = 92^{\circ}$.

Answer:

$m\angle a = 92^{\circ}$, $m\angle c=92^{\circ}$, $m\angle h = 92^{\circ}$