Question

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

Explanation:

Step1: Identify vertical - angle relationship

The 150 - degree angle and ∠1 are vertical angles. Vertical angles are congruent.
So, $m\angle1 = 150^{\circ}$

Step2: Identify linear - pair relationship

∠1 and ∠2 form a linear pair. The sum of angles in a linear pair is 180°.
So, $m\angle2=180 - m\angle1$
Substitute $m\angle1 = 150^{\circ}$ into the equation: $m\angle2 = 180 - 150=30^{\circ}$
The theorem for ∠1 is the Vertical Angles Theorem. The theorem for ∠2 is the Linear - Pair Postulate.

Answer:

$m\angle1 = 150^{\circ}$, $m\angle2 = 30^{\circ}$; Vertical Angles Theorem for ∠1, Linear - Pair Postulate for ∠2