SOLUTION: The supplement of an angle is 26 more than 5 times its complement. Find the measure of the angle. I need this explained thoroughly, so I can figure out similar problems! Thank

Question 500266: The supplement of an angle is 26 more than 5 times its complement. Find the measure of the angle.
I need this explained thoroughly, so I can figure out similar problems! Thank you!
ASAP would be nice too!
Thanks!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The supplement of an angle is 26 more than 5 times its complement.
Find the measure of the angle.
:
Let x = the angle
then
(180-x) is the supplement of x
and
(90-x) is the complement of x
:
With this information, write an equation for the statement
"The supplement of an angle is 26 more than 5 times its complement."
(180-x) = 26 + 5(90-x)
180 - x = 26 + 450 - 5x
-x + 5x = 26 + 450 - 180
4x = 296
x =
x = 74 degrees is the angle
:
:
See if the satisfied the statement;
The supplement of an angle is 26 more than 5 times its complement.
(180-74) = 26 + 5(90-74)
106 = 26 + 5(16)
106 = 26 + 80; confirms our solution
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