SOLUTION: the supplement of an angle is four times the complement of the angle. Find the measure of the complement.

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Question 212985This question is from textbook Geometry for the ejoyment and challenge
: the supplement of an angle is four times the complement of the angle. Find the measure of the complement. This question is from textbook Geometry for the ejoyment and challenge

Found 2 solutions by drj, MathTherapy:
Answer by drj(1380) (Show Source):
You can put this solution on YOUR website!
The supplement of an angle is four times the complement of the angle. Find the measure of the complement.

Step 1. Supplement is when two angles add up to 180 degrees or A+B=180

where A be one angle and B be the other complementary angle.

Step 3. A=4B (supplement of an angle is four times the complement of the angle)

Step 4. Substitute A=4B into Step 1.

Step 5. Angles are 36 and 144. The complement is 36 degrees as stated in the problem.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!
the supplement of an angle is four times the complement of the angle. Find the measure of the complement.

Let the angle be A
Then the supplement of the angle is (180 - A), and the complement of the angle is (90 - A)

Since the supplement is four times the complement, then we'll have:

180 - A = 4(90 - A)

180 - A = 360 - 4A

3A = 180

Since A, or the angle is , then its complement is 90 - 60 =
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Check
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Angle = . Therefore, its supplement = (180 - 60)
Also, its complement is (90 - 60)
So, since its supplement is equal to 4 times its complement, then:
, or, ---TRUE---