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 :

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

$therefore x=90-28=62$ .