Question

What is the measure of <1?

Answer 1

∠ 1 = 72°

Explanation:

(4n - 2) and (2n + 17) are adjacent angles and sum to 180° , that is

4n - 2 + 2n + 17 = 180

6n + 15 = 180 ( subtract 15 from both sides )

6n = 165 ( divide both sides by 6 )

n = 27.5

Then

2n + 17 = 2(27.5) + 17 = 55 + 17 = 72

∠ 1 and 2n + 17 are vertical angles and congruent , so

∠ 1 = 72°