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Blababa [14]
3 years ago
12

Solve with a system of equations: Two angles are supplementary if the sum of their measures are 180 degrees. If one is 90 degree

s more than twice the measure of the other angle, what are the measures of the angles?
Mathematics
1 answer:
julsineya [31]3 years ago
6 0

Answer:

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

Step-by-step 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

___

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°.

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