Question

∠A and \angle B∠B are supplementary angles. If m\angle A=(x+26)^{\circ}∠A=(x+26) ∘ and m\angle B=(2x+22)^{\circ}∠B=(2x+22) ∘ , then find the measure of \angle B∠B.

Answer 1

110°

Explanation:

The question tells us the angle A and angle B are supplementary angles. This means that the sum of the two angles is 180°.

Set up an Equation and Solve for X

Using this information, we can set up an equation.

Angle A + Angle B = 180

`(x+26)+(2x+22)=180\\x+26+2x+22=180`Combine like Terms

`3x+48=180` Subtract both sides by 48

`3x=132` Divide both sides by 3

`x=44`

Find the Measure of Angle B

We can substitute 61 for x into the given equation for Angle B.

Angle B = 2x + 22

Angle B = 2(44) + 22

Angle B = 88 + 22

Angle B = 110

Check your Work

Angle A + Angle B = 180

44 + 26 + 2(44) + 22 = 180

70 + 88 + 22 = 180

158 + 22 = 180

180 = 180

Therefore ∠B = 110°.