Question

parallel lines & transversals schoology assignment if m || n and m∠e = 94° in the figure to the right, find the measures of ∠a, ∠c, and ∠h. m∠a= m∠c= m∠h=

Explanation:

Step1: Identify vertical - angle relationship

$\angle a$ and $\angle c$ are vertical angles. $\angle e$ and $\angle g$ are vertical angles, $\angle h$ and $\angle f$ are vertical angles. Vertical angles are equal. Also, $\angle e$ and $\angle a$ are corresponding angles when $m\parallel n$.

Step2: Find $\angle a$

Since $m\parallel n$, $\angle a$ and $\angle e$ are corresponding angles. Corresponding angles formed by parallel lines and a transversal are equal. So $m\angle a=m\angle e = 94^{\circ}$.

Step3: Find $\angle c$

$\angle a$ and $\angle c$ are vertical angles. Vertical angles are congruent. So $m\angle c=m\angle a = 94^{\circ}$.

Step4: Find $\angle h$

$\angle e$ and $\angle h$ are supplementary (linear - pair). The sum of angles in a linear - pair is $180^{\circ}$. So $m\angle h=180^{\circ}-m\angle e=180 - 94=86^{\circ}$.

Answer:

$m\angle a = 94^{\circ}$
$m\angle c = 94^{\circ}$
$m\angle h = 86^{\circ}$