∠A and \angle B∠B are vertical angles. If m\angle A=(7x+22)^{\circ}∠A=(7x+22)
∘
and m\angle B=(8x+20)^{\circ}∠B=(8x+20)
∘
, then find the measure of \angle A∠A.

Two angles that are vertically opposite to each other are called vertical angles, and they have congruent angle measures. That is, vertical angles are equal.

Angles A and B are vertical angles, then, they are equal to each other.

m<A = (7x + 22)°

m<B = (8x + 20)°

m<A = m<B

Substitute

7x + 22 = 8x + 20

7x - 8x = -22 + 20

-x = -2

x = 2

m<A = 7x + 22

Plug in the value of x

m<A = 7(2) + 22

m<A = 14 + 22

m<A = 36°

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∠A and \angle B∠B are vertical angles. If m\angle A=(7x+22)^{\circ}∠A=(7x+22) ∘ and m\angle B=(8x+20)^{\circ}∠B=(8x+20) ∘ , then find the measure of \angle A∠A.

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What are Vertical Angles?

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∠A and \angle B∠B are vertical angles. If m\angle A=(7x+22)^{\circ}∠A=(7x+22)
∘
and m\angle B=(8x+20)^{\circ}∠B=(8x+20)
∘
, then find the measure of \angle A∠A.