SOLUTION: The measure of the supplement of an angle is 10 percent more than four times the measure of the angle. Find the measures of both angles.

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Question 151591: The measure of the supplement of an angle is 10 percent more than four times the measure of the angle. Find the measures of both angles.
Answer by jojo14344(1512) About Me  (Show Source):
You can put this solution on YOUR website!
We all know supplementary angles are 2 angles that add to 180 degrees.
For that reason, we can make an equation A%2BB=180 ---------> eqn 1
It shows angle B is a supplemantary of angle A, and to satisfy the other condition 1 being 10percent more than 4times it's measure angle.
Putting that into eqn, A=4B%2A1.10, right? ------> eqn 2
We multiply by 1.10 because it's 10percent more.
.
Substitute eqn 2 in eqn 1 we have
%284B%29%281.10%29%2BB=180
4.40B%2BB=180
5.40B=180 ---------> cross%285.40%29B%2Fcross%285.40%29=cross%28180%2933.33333%2Fcross%285.40%29
B=33.333333deg
The other angle as per eqn 1: A%2B33.333333=180 ----> A=146.666667deg
To check:
As it stated the supplement angle 10percent more than 4times it's measurement,go back eqn 2,
146.666667=4%2833.33333%29%2A1.10
146.6666667=146.6666667
Also, in eqn 1
A%2BB=180 ------------> 146.666667%2B33.33333=180
180=180
Thank you,
Jojo