SOLUTION: two angles are supplementary. one angle measure is 22 more than the other. find the measure of the angles

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Question 695136: two angles are supplementary. one angle measure is 22 more than the other. find the measure of the angles
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Supplementary Angles add up to 180°.

let alpha and beta be supplementary angles

so, alpha%2Bbeta=180°........1

given: alpha is 22 more than the beta

so, alpha=beta%2B22°........2

go to alpha%2Bbeta=180°........1 and plug in alpha

beta%2B22%2Bbeta=180°....solve for beta

2beta%2B22=180°

2beta=180-22°

2beta=158°

beta=158%2F2°

highlight%28beta=79%29°

now find alpha

alpha%2Bbeta=180°........1

alpha%2B79=180°

alpha=180-79°
highlight%28alpha=101%29°