Question

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

\qquad \blueD{\angle A=6x + 5^\circ}∠A=6x+5
∘
start color #11accd, angle, A, equals, 6, x, plus, 5, degrees, end color #11accd \qquad\green{\angle B=4x + 45^\circ}∠B=4x+45
∘
start color #28ae7b, angle, B, equals, 4, x, plus, 45, degrees, end color #28ae7b

Answer 1

∠A = 125 degrees.

Explanation:

Look at attachment:

Hope this helps! :)

Answer 2

x = 20, ∠ A = 125°

Explanation:

∠ A and ∠ B are Alternate interior angles and are congruent, so

∠ A = ∠B , substitute values

6x + 5 = 4x + 45 ( subtract 4x from both sides )

2x + 5 = 45 ( subtract 5 from both sides )

2x = 40 ( divide both sides by 2 )

x = 20

Thus

∠ A = 6x + 5 = 6(20) + 5 = 120 + 5 = 125°