Both angles are consecutive interior angles, m∠1 measures 72° while m∠2 measures 108°.
A pair of consecutive interior angles is formed when a transversal cuts two parallel lines. This pair of consecutive interior angle are supplementary.
Therefore we can say that:
m∠1 + m∠2 = 180° (consecutive interior angles are supplementary)
Therefore substituting gives:
(2x + 6) + (3x + 9) = 180
2x + 3x + 6 + 9 = 180
5x + 15 = 180
5x = 165
x = 33°
hence, m∠1 = 2x + 6 = 2(33) + 6 = 72°
m∠2 = 3x + 9 = 3(33) + 9 = 108°
Therefore m∠1 measures 72° while m∠2 measures 108°.
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