Question

Lines b and c are parallel.
Which is the measure of 6

Answer 1

m∠6 = 54°

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°