Question

\angle A∠A and \angle B∠B are vertical angles. If m\angle A=(8x-23)^{\circ}∠A=(8x−23) ∘ and m\angle B=(6x-5)^{\circ}∠B=(6x−5) ∘ , then find the measure of \angle A∠A.

Answer 1

∠A = 49°

Explanation:

Vertically opposite angles are congruent.

∠A = ∠B

8x - 23 = 6x - 5

Add 23 to both sides,

8x = 6x - 5 + 23

8x = 6x + 18

Subtract 6x from both sides,

8x - 6x = 18

2x = 18

Divide both sides by 2,

x = 18 ÷ 2

x = 9

∠A = 8x - 23

= 8*9 - 23

= 72 - 23

= 49°