find the measure of angle whose supplement is 10 times its complement

Question

find the measure of angle whose supplement is ten times its complement
hint : supplement and complement of an angles are (180-0)^0 and (90-0)^0

Answer 1

Try to write out exactly what it says, in "algebra":

 

"find the measure of angle" -- They want you to find the angle, so call the angle x

"whose supplement" -- that's 180 - x

"is" -- that means, equals or =

"10 times" -- 10 *

"its complement" -- that's 90 - x

 

So that gives you an equation:

 

180 - x = 10 * (90 - x)

 

Just solve it...

 

180 - x = 10 * (90 - x)

180 - x = 900 - 10x

180 - x + 10x - 900

180 + 9x = 900

9x = 720

x = 80

 

So the angle is 80°.  Check the answer by seeing if the statement about the angle is correct.