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 ( mangle7 = 94^circ ). ∠8 and ∠10 are alternate interior angles. find the measure of ∠10.

Explanation:

Step1: Find measure of ∠8

Since ∠7 and ∠8 are consecutive interior angles (supplementary, sum to \(180^\circ\)) and \(m\angle7 = 94^\circ\), we use \(m\angle7 + m\angle8 = 180^\circ\).
So, \(m\angle8 = 180^\circ - 94^\circ = 86^\circ\).

Step2: Find measure of ∠10

∠8 and ∠10 are alternate interior angles. For parallel lines cut by a transversal, alternate interior angles are congruent.
Thus, \(m\angle10 = m\angle8 = 86^\circ\).

Answer:

86