Question

find m∠1 and m∠2. tell which theorem can be used.

m∠1 =

by the

m∠2 =

by the

30° 150° corresponding angles theorem alternate exterior angles theorem consecutive interior angles theorem alternate interior angles theorem

Explanation:

Step1: Identify angle - relationship for ∠1

The 150 - degree angle and ∠1 are corresponding angles. By the Corresponding Angles Theorem, corresponding angles are congruent when two parallel lines are cut by a transversal.
So, $m\angle1 = 150^{\circ}$

Step2: Identify angle - relationship for ∠2

∠1 and ∠2 are supplementary angles (linear - pair). The sum of angles in a linear - pair is 180°. So, $m\angle2=180 - m\angle1$. Substituting $m\angle1 = 150^{\circ}$, we get $m\angle2 = 180 - 150=30^{\circ}$

Answer:

$m\angle1 = 150^{\circ}$ by the Corresponding Angles Theorem
$m\angle2 = 30^{\circ}$ by the Linear - Pair Postulate (or the fact that the sum of angles in a linear - pair is 180°)