supplement and complement

The supplement of an angle is 60 degrees less than twice the supplement of the complement of the angle. Find the measure of the complement.



I know the answer is 70 degrees because i looked in the back of the book but i need to know how to solve it. Thanks for your help

ash4 said:

The supplement of an angle is 60 degrees less than twice the supplement of the complement of the angle. Find the measure of the complement.

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What is the name of the angle? You don't know? Oh, well, then, I guess we should give it a name.

x = The Angle we are looking for.

Supplementary Angles add to 180º
Complementary Angles add to 90º

Decode one piece at a time.

"The supplement of an angle" That's (180º - x)
"The complement of an angle" That's (90º - x)
"the supplement of the complement of the angle" That's [180º - (90º - x)]

"The supplement of an angle is 60 degrees less than twice the supplement of the complement of the angle."

"(180º - x) is 60 degrees less than twice the supplement of the complement of the angle."

"(180º - x) is 60 degrees less than twice [180º - (90º - x)]"

Can you finish?

yes, i can. thank you soooooooooo much i love you!

Please explain again. I have a problem too. It is an angle is 3 times its complement. Find the two angles

mrmscheergirl said:

Please explain again. I have a problem too. It is an angle is 3 times its complement. Find the two angles

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A slightly different approach than the one Sir Denis suggested:

let x = measure of the angle
then, 90 - x = measure of the complement

(I like this "beginning" because you can use it on ANY complementary angles problem)

Ok....the problem says

the measure of the angle is 3 times the measure of the complement

x = 3*(90 - x)

Now, can you solve that for x? That (as we've stated) is the measure of the angle, and 90 - x is the measure of the complement.