SOLUTION: The supplement of an angle is four times the complement of the angle. Find the measure of the complement. <1=x <2=4x <1+<2=180 degrees dont get how to add in the complementar

Algebra ->  Angles -> SOLUTION: The supplement of an angle is four times the complement of the angle. Find the measure of the complement. <1=x <2=4x <1+<2=180 degrees dont get how to add in the complementar      Log On


   

Question 222083: The supplement of an angle is four times the complement of the angle. Find the measure of the complement.
<1=x
<2=4x
<1+<2=180 degrees
dont get how to add in the complementary
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
There are a couple of ways to do this one. I think since you have supplement AND complement in this problem, I would

let x = the angle. Then,
90-x = the complement
180-x = the supplement

Write the equation this way:

Supplement IS 4 times Complement
180-x = 4(90-x)
180-x = 360-4x

Add +4x to each side:
180-x+4x= 360-4x+4x
180+3x = 360

Subtrac 180 from each side:
3x = 180
x= 60 the angle

The complement is 90-x = 30 degrees
The supplement is 180-x = 120 degrees

Answer the question: "Find the measure of the complement." The answer to the problem is 30 degrees.

Check: "The supplement is 4 times the complement." This is true!

R^2

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