Supplementary and Complementary Angles

Question

The measure of the supplement of an angle is five times the measure of its complement.

 

The measure of the angle is ____, the measure of its complement is _____, and the measure of its supplement is _____.

What do I put in the blanks? How do I figure this out?

Answer 1

Let x be the angle, then

180-x is the supplement and 90-x is the complement so that

180-x = 5(90-x)

180-x=450-5x

You should be able to finish it from here.

Answer 2

Paul M is correct!

Another way is

C = complement of the angle in degrees

A = the unknown angle in degrees

S = supplement of the angle in degrees

Equation for five times the complement of the angle is equal to the supplement

5C + A = 180°

therefore

the complement of the angle is equal to 90 degrees minus A(unknown angle)°

C = 90° - A

Now replace 90° - A for C in the first equation.

5(90° - A) + A = 180°

Distributive (5 x 90°) - 5(A)

450° - 5A + A = 180°

Combine like terms

450° - 4A = 180°

450° - 180° - 4A + 4A = 180° - 180° + 4A

Combine like term again

270° = 4A

270°/4 = 4A/4

67.5° = A

Now fill in to find the complementary and supplementary angles.

5C + A = 180

5C + 67.5° = 180

-67.5 = -67.5‾

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5C = 112.5°

5C / 5 = 112.5° / 5

C = 22.5

5C = S

5(22.5°) = S

112.5° = S

The measure of the angle is 67.5 °, the measure of its complement is 22.5°, and the measure of its supplement is 112.5°.