Question

use a model lines a and b are parallel and are cut by transversal t to form interior angles ∠7, ∠8, ∠9, and ∠10.∠7 and ∠8 are consecutive interior angles, and m∠7 = 94°.∠8 and ∠10 are alternate interior angles. find the measure of ∠10.

Explanation:

Step1: Recall angle - relationship property

Consecutive interior angles are supplementary. Since $\angle7$ and $\angle8$ are consecutive interior angles and $m\angle7 = 94^{\circ}$, then $m\angle7+m\angle8 = 180^{\circ}$.
$94^{\circ}+m\angle8=180^{\circ}$

Step2: Solve for $m\angle8$

Subtract $94^{\circ}$ from both sides of the equation.
$m\angle8=180^{\circ}- 94^{\circ}=86^{\circ}$

Step3: Use alternate - interior angles property

Alternate interior angles are congruent. Since $\angle8$ and $\angle10$ are alternate interior angles, $m\angle8 = m\angle10$.

Answer:

$86^{\circ}$