SOLUTION: the sum of the measures of an obtuse and an acute angle is 160. the sum of the complement of the acute angle and one-half the supplement of the obtuse angle is 75. find the measure

Algebra ->  Angles -> SOLUTION: the sum of the measures of an obtuse and an acute angle is 160. the sum of the complement of the acute angle and one-half the supplement of the obtuse angle is 75. find the measure      Log On


   

Question 471065: the sum of the measures of an obtuse and an acute angle is 160. the sum of the complement of the acute angle and one-half the supplement of the obtuse angle is 75. find the measures of the two angles.
Answer by gsmani_iyer(201) About Me  (Show Source):
You can put this solution on YOUR website!
Let the obtuse angle be = x
Let the acute angle be = y
x + y = 160 ....... ........ (1)
%28%28180-x%29%2F%282%29%29%2B%2890-y%29+=+75
90-%28x%29%2F%282%29%2B+90-y+=+75
180+-+75+=+%28x%29%2F%282%29+%2B+y
105+=+%28x%29%2F%282%29+%2B+y ......... ........Multiplying both the sides by 2, we get:
x+%2B+2y+=+210 ........ ........ (2)
From Eqn.(2) - (1) we get,
y+=+50
Applying y's value in Eqn.(1), we get
x + 50 = 160; So, x = 160 - 50 = 110.
So, the measure of obtuse angle = 110 ;
and the measure of acute angle = 50. Answer.

I hope you have understood the above solution. All the best.
gsm