SOLUTION: The sum of the measures an obtuse angle & an acute angle is 160 . the sum of the complement of the acute angle & 1/2 the supplement of the obtuse angle is 75 .find the measures of

Question 330821: The sum of the measures an obtuse angle & an acute angle is 160 . the sum of the complement of the acute angle & 1/2 the supplement of the obtuse angle is 75 .find the measures of two angles.
Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
two angles are complement of each other if they add to 90 degrees
Two angels are supplement of each other if the add to 180 degrees
Let A=acute angle, O=Obtuse angle
then complement of A = 90-A, supplement of O = 180-O
You are given
1) A+O =160
2) (90-A)+1/2(180-O)=75 You have two equations and two unknowns
simplify the second equation:
90-A+90-O/2=75
105=A + O/2
from first equation solve for A=160-O and substitute in 105=A+O/2
105=160-O+O/2
-55=-O/2
110=O and A=160-O=50
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