SOLUTION: Find the degree measure of an angle whose complement is 25 percent of its supplement.

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Question 222800: Find the degree measure of an angle whose complement is 25 percent of its supplement.
Answer by drj(1380) About Me  (Show Source):
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Find the degree measure of an angle whose complement is 25 percent of its supplement.

Step 1. Complementary angles means two angles add up 90 degrees.

Step 2. Supplementary angles means two angles add up 180 degrees.

Step 3. Let x be the angle

Step 4. Let 90-x be the complementary angle

Step 5. Let 180-x be the supplementary angle.

Step 6. Let 25% be 1/4=0.25 by definition

Step 7. Then 90-x=%28180-x%29%2F4 since measure of an angle whose complement is 25 percent of its supplement.

Step 8. Solving equation in Step 7 yields the following steps...

90-x=%28180-x%29%2F4

Multiply by 4 to both sides of the equation

4%2890-x%29=180-x

360-4x=180-x

Add 4x-180 to both sides of the equation

360-4x%2B4x-180=180-x%2B4x-180

180=3x

Divide by 3 to both sides of the equation

180%2F3=3x%2F3

x=60 Then 90-x=30 and 180-60=120 and the complementary angle of 30 degrees is equal to 25 percent of the supplementary angle of 120 degrees

Step 9. ANSWER: The angle is 60 degrees.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J