Question

angle a and angle b are complementary angles. If angle A= (2x-13) degrees and angle B=(2x+7) degrees, then find the measure of angle A

Answer 1

Angle A = 35

Explanation:

When angles are complementary, this means they add up to 90 degrees. If we want to find the value of angle A, we need to first find out what the unknown variable x is before we can evaluate for A. We can do this by writing an equation.

`(2x-13)+(2x+7)=90`

Combine like terms

`4x-6=90`

Add 6 to both sides

`4x=96`

Divide by 4

`x=24`

X is 24. Now we just plug in 24 and evaluate for A.

`A=2(24)-13`

Multiply

`A=48-13`

Subtract

`A=35`

To check our work, we can also find B and evaluate

`B=55`

`55+35=90`

Answer 2

m∠A = 35°

Explanation:

∠A and ∠B are complementary angles, meaning their sum is 90°.

(2x-13) + (2x + 7) = 90

4x - 6 = 90

4x = 96

x = 24

Substitute 24 for x in ∠A's equation.

2(24) - 13 = 48 - 13 = 35°

m∠A = 35°