Question 500266
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 = {{{296/4}}}
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