Answer:
The measure of Angle 6 is 57 degrees.
Step-by-step explanation:
Angle 1 is congruent to Angle 5 (6x + 159) via the Corresponding Angles Theorem.
Angle 1 is supplementary to Angle 2 (-7x + 15).
Due to the transitive property, Angle 5 (6x + 159) and Angle 2 (-7x + 15) are supplementary.
Set them to 180.
-x + 174 = 180
Subtract 174 from both sides.
-x = 6
Divide -1 on both sides.
x = -6
Substitute -6 for Angle 5's value.
6(-6) + 159
-36 + 159
Angle 5 is 123 degrees.
Since Angle 6 is next to Angle 5, they are supplementary.
180 - 123 = 57
