Question

Solve with a system of equations: Two angles are supplementary if the sum of their measures are 180 degrees. If one is 90 degrees more than twice the measure of the other angle, what are the measures of the angles?

Answer 1

The measures of the angles are 150° and 30°.

Explanation:

Let x and y represent the measures of the angles, with x representing the larger angle.

x + y = 180 . . . . . . the two angles are supplementary

x = 90 + 2y . . . . . one is 90° more than twice the other

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Substituting the expression given by the second equation into the first, we have ...

(90 +2y) +y = 180

3y = 90 . . . . . . . . . . collect terms, subtract 90

y = 30 . . . . . . . . . . . divide by the coefficient of y

x = 180 -y = 150

The measures of the angles are 150° and 30°.