Answer:
m∠6 = 54°
Step-by-step explanation:
Given the diagram, we know that line b is a straight line and angles 1 (the angle measuring 13x + 9°) and 2 are supplementary angles and thus add up to 180.
We also know angles 2 and 7 (the angles measuring 5x + 9°) are alternate exterior angles and are therefore congruent.
So since angle 2 = 5x + 9, we can do:
13x + 9 + 5x + 9 = 180
18x + 18 = 180
18x = 162
x = 9
Angles 7 and 6 are also congruent plugging x into angle 7 also gives us the measure of angle 6:
5(9) + 9 = 45 + 9 = 54°
