m<6 = 117° based on the same-side-interior angles theorem
m<7 = 63° based on the corresponding angles theorem
What is the Same-Side Interior Angles Theorem?
Angles 3 and 6 are same-side interior angles, therefore, based on the same-side-interior angles theorem, their sum equals 180 degrees because they are supplementary to each other.
Thus:
m<3 + m<6 = 180
Substitute
63 + m<6 = 180
m<6 = 180 - 63
m<6 = 117°
m<7 = m<3 [corresponding angles theorem]
m<7 = 63°
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