Question

∠A and \angle B∠B are supplementary angles. If m\angle A=(2x-9)^{\circ}∠A=(2x−9) ∘ and m\angle B=(2x+21)^{\circ}∠B=(2x+21) ∘ , then find the measure of \angle A∠A.

Answer 1

Answer: 75 degrees

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Work Shown:

A+B = 180 since the angles are supplementary

(2x-9)+(2x+21) = 180

4x+12 = 180

4x = 180-12

4x = 168

x = 168/4

x = 42

Then,

• A = 2x-9 = 2*42-9 = 75 degrees
• B = 2x+21 = 2*42+21 = 105 degrees

As a check, A+B = 75+105 = 180 to confirm the answer.