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∠A and ∠ B ∠B are complementary angles. If m ∠ A = ( 2 x − 10 ) ∘ ∠A=(2x−10) ∘ and m ∠ B = ( x − 2 ) ∘ ∠B=(x−2) ∘ , then find the measure of ∠ A ∠A.

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Answer:

Angle A = 58 degrees

Angle B = 32 degrees

Step-by-step explanation:

First of all, we will need to know that complementary angles are angles that sum up to 90 degrees.

This means that if we add the values of angle A and angle B, they will both sum up to 90 degrees.

i.e (2x-10) + (x-2) = 90

3x -12 = 90

3x = 102

x = 34 degrees

We can substitute this value of x into the equations for angles A and B

A = (2 X (34) - 10 ) = 58 degrees

B =  ( 34 - 2) = 32 degrees

Therefore, angles A and B are 54 and 32 degrees respectively.

Check: We can add the two angles to see if we get 90 degrees. 58 + 32 = 90 degrees. This shows that the two angles are complementary and our answer is correct.

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