SOLUTION: The measure of the supplement of an angle exceeds five times the measure of the complement of the angle by ten. Find the measure of the original angle.

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Question 322822: The measure of the supplement of an angle exceeds five times the measure of the complement of the angle by ten. Find the measure of the original angle.
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the angle
90-x= the complement
180-x = the supplement

Paraphrasing the statement to write the equation:
The supplement IS 10 more than 5 times the complement.
180-x=5(90-x)+10
180-x=450-5x+10
180-x+5x=460-5x+5x
180+4x=460
4x=460-180
4x=280
x=70 = the angle
90-x=20 the complement
180-x=180-70=110 the supplement

Check:
The supplement 110 exceeds 5 times the complement 20 by 10
110 = 100 + 10
It checks!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus