Question

∠A=10x+24 ∘ start color #11accd, angle, A, equals, 10, x, plus, 24, degrees, end color #11accd \qquad \green{\angle B=6x + 72^\circ}∠B=6x+72 ∘ start color #28ae7b, angle, B, equals, 6, x, plus, 72, degrees, end color #28ae7b Solve for xxx and then find the measure of \blueD{\angle A}∠Astart color #11accd, angle, A, end color #11accd:

Answer 1

Answer:

x = 12

The measure of Angel A and Angle B = 144°

Step-by-step explanation:

Angle ∠ A= 10x+24∘

Angle ∠B=6x+72 ∘

Angle A and Angle B are Alternate interior angles hence, they are equal to each other.

Hence:

10x + 24 = 6x + 72

Collect like terms

10x - 6x = 72 - 24

4x = 48

x = 48/4

x = 12

The measure of ∠ A= 10x+24∘

=( 10(12) + 24)°

=( 120 + 24)°

= 144°

The Measure of Angle ∠B=6x+72 ∘

=( 6(12) + 72)°

= (72 + 72)°

= 144°