∠A and \angle B∠B are complementary angles. If m\angle A=(2x-10)^{\circ}∠A=(2x−10) ∘ and m\angle B=(x-2)^{\circ}∠B=(x−2) ∘ , then find the measure of \angle A∠A.

118°

Step-by-step explanation:

Two angles are called complementary when their measures add to 90 degrees.

From the question,

Angle A=(2x-10)°

Angle B=(x-2)°

Both Angles are complementary.

Therefore

Step 1

(2x - 10)° + (x - 2)° = 180°

2x + x - 10 - 2 = 180°

3x - 12 = 180°

3x = 180° + 12

3x = 192°

x = 192/3

x = 64°

Step 2

We are to solve for Angle A

(2x-10)°

Angle A = 2(64 ) - 10

Angle A = 128 - 10

Angle A = 118°

The measure of Angle A = 118°

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