SOLUTION: Two angles are complementary, and one angle has a measure that is nine times the measure of the other angle. What is the measure of the larger angle?

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Question 1168167: Two angles are complementary, and one angle has a measure that is nine times the
measure of the other angle. What is the measure of the larger angle?
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52801) About Me  (Show Source):
You can put this solution on YOUR website!
.

x + 9x = 90  degrees


10x    = 90

  x    = 90/10 = 9 degrees.


ANSWER.  The larger angle is 9*9 = 81 degrees.

Solved.

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    - Angles basics
    - HOW TO solve problems on supplementary, complementary or vertical angles - Examples
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Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x be the smaller angle.
then 9x is the larger angle.

if the angles are complementary, then their sum is 90 degrees.

you get x + 9x = 90

combine like terms to get 10x = 90

solve for x to get x = 9

the smaller angle is 9 degrees.

the larger angle is 9 times that = 81 degrees.

their sum is 90 degrees, confirming the solution is correct.

the solution is that the larger angle measures 81 degrees.