# Thread: Supplement and Complementary angle problem

1. ## Supplement and Complementary angle problem

1. The ratio of the measure of the supplement of an angle to
that of the complement of the angle is 5:2. Find the
measure of the supplement.

Not sure how to set it up.

2. ## Re: Supplement and Complementary angle problem

I got the idea.

5(90 - x) = 2(180 - x)
450 - 5x = 360 - 2x
90 = 3x
30 = x

180 - 30 = 150

Why would i get a different answer is I set it up as
5(180 - x) = 2(90 -x) ?

What is the key part in the question that makes our expression be 5(90 -x) = 2(180 -x)

3. ## Re: Supplement and Complementary angle problem

Originally Posted by Cake
I got the idea.

5(90 - x) = 2(180 - x)
450 - 5x = 360 - 2x
90 = 3x
30 = x

180 - 30 = 150

Why would i get a different answer is I set it up as
5(180 - x) = 2(90 -x) ?

What is the key part in the question that makes our expression be 5(90 -x) = 2(180 -x)
the wording is pretty clear

supplement is (180-x)
complement is (90-x)

it says the ratio of the measure of the supplement of an angle to that of the complement, i.e.

(180-x)/(90-x)

is 5:2, i.e.

5/2

so the problem states that

(180-x)/(90-x) = 5/2 ==> 2(180-x) = 5(90-x)

it doesn't state it the other way around and they aren't the same equation so you should expect a different answer.

4. ## Re: Supplement and Complementary angle problem

Originally Posted by romsek
the wording is pretty clear

supplement is (180-x)
complement is (90-x)

it says the ratio of the measure of the supplement of an angle to that of the complement, i.e.

(180-x)/(90-x)

is 5:2, i.e.

5/2

so the problem states that

(180-x)/(90-x) = 5/2 ==> 2(180-x) = 5(90-x)

it doesn't state it the other way around and they aren't the same equation so you should expect a different answer.
Perfect. Thank you.