Question

The angle measurements in the diagram are represented by the following expressions.

\qquad \blueD{\angle A= 5x - 5^\circ}∠A=5x−5
∘
start color #11accd, angle, A, equals, 5, x, minus, 5, degrees, end color #11accd \qquad \greenD{\angle B= 3x + 13^\circ}∠B=3x+13
∘
start color #1fab54, angle, B, equals, 3, x, plus, 13, degrees, end color #1fab54

Answer 1

x = 9, ∠ B = 40°

Explanation:

∠ A and ∠ B are corresponding angles and congruent, so

5x - 5 = 3x + 13 ( subtract 3x from both sides )

2x - 5 = 13 ( add 5 to both sides )

2x = 18 ( divide both sides by 2 )

x = 9

Then

∠ B = 3x + 13 = 3(9) + 13 = 27 + 13 = 40°