Answer:
m∠1 = 126°
m∠2 = 154°
Explanation:
First, find the measure of angle that is supplementary to ∠1. (I will call it ∠A)
We know that the measures of the interior angles of a triangle add to 180°.
Therefore,
m∠A + 96° + 30° = 180°
m∠A + 96° = 150°
m∠A = 54°
From this value, we can solve for m∠1, since it is supplementary to ∠A:
m∠A + m∠1 = 180°
54° + m∠1 = 180°
m∠1 = 126°
To solve for ∠2, we must first solve for the adjacent supplementary angle that I have named ∠B.
First, the measures of the interior angles of a triangle add to 180°:
28° + m∠1 + m∠B = 180°
28° + 126° + m∠B = 180°
m∠B = 26°
Finally, we can solve for m∠2 because it is supplementary to ∠B.
m∠B + m∠2 = 180°
26° + m∠2 = 180°
m∠2 = 154°