Question

The sum of the measures of two complementary angles is 90 degrees. If one angle measures 39 degrees more than 2 times the measure of its​ complement, find the measures of the two angles.

Answer 1

Let 'x' and 'y' be two complementary angles.

The sum of two complementary angles is always 90 degrees.

So, $x+y = 90^\circ$  

$y = 90^\circ - x$   (equation 1)

It is given that, one angle measures 39 degrees more than 2 times the measure of its complement.

So, $x = 39^\circ+(2 \times y)$

$x = 39^\circ+2y$

Substituting the value of 'y' from equation 1 in the above equation, we get

$x = 39^\circ+2(90^\circ-x)$

$x=39^\circ+180^\circ-2x$

$x + 2x = 219^\circ$

$3x = 219^\circ$

So, $x = 73^\circ$

Since, $y = 90^\circ-x$

$y = 90-73 = 17^\circ$

Therefore, the measure of two angles are $73^\circ$ and  $17^\circ$.