The measure of angle 3 is 100°. option C
m ∠ 3 = 100°
What is m ∠ 3?
m ∠ 2 = 8x + 12
m ∠ 8 = 10x - 30
Same-side exterior angles are supplementary, meaning that they have a sum of 180 degrees
m ∠ 2 + m ∠ 8 = 180°
8x + 12 + 10x - 30 = 180°
18x - 18 = 180
18x = 180 + 18
18x = 198
Divide both sides by 18
x = 198/18
x = 11
So,
m ∠ 2 = 8x + 12
= 8(11) + 12
= 88 + 12
m ∠ 2 = 100°
Therefore,
m ∠ 2 = m ∠ 3
Vertical opposite angles are equal
m ∠ 3 = 100°