Two angles are complementary. The sum of the measure of the first angle and one-fourth the second angle is 69 degrees. What is the measures of the angles?

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Answer 1 · 2016-01-09T18:56:56

#62^@ and 28^@#

Let the 2 unknown angles be #x and y#.

Since they are complimentary, #x+y=90^@#.

But, from the other given information, #x+1/4y=69#.

These are now 2 equations in 2 unknowns which may be solved simultaneously to get :

#x=90-y#
#therefore (90-y)+1/4y=69#
#therefore y=(90-69)/(1-1/4)=28#.

#therefore x=90-28=62#.