Question

segments, lines and angles finding angle measures given two parallel lines cut by a transversal two parallel lines are cut by a transversal as shown below. suppose m∠2 = 98°. find m∠5 and m∠7.

Explanation:

Step1: Identify angle - relationship for ∠5

∠2 and ∠5 are alternate interior angles. When two parallel lines are cut by a transversal, alternate - interior angles are congruent.
$m\angle5 = m\angle2$

Step2: Substitute the value of ∠2

Since $m\angle2 = 98^{\circ}$, then $m\angle5=98^{\circ}$

Step3: Identify angle - relationship for ∠7

∠2 and ∠7 are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are congruent.
$m\angle7 = m\angle2$

Step4: Substitute the value of ∠2

Since $m\angle2 = 98^{\circ}$, then $m\angle7 = 98^{\circ}$

Answer:

$m\angle5 = 98^{\circ}$
$m\angle7 = 98^{\circ}$