∠A and \angle B∠B are vertical angles. If m\angle A=(4x-19)^{\circ}∠A=(4x−19) ∘ and m\angle B=(5x-28)^{\circ}∠B=(5x−28) ∘ , then find the value of x.

Answer 1

Vertical angles are always congruent. Therefore, the measure of the two angles should be equal:

m∠A = m∠B

4x-19 = 5x-28

Then solve for x:

4x-19 = 5x-28

-19 = x-28

9 = x