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 itsâ€‹ complement, find the measures of the …

Question

asked Sep 26, 2019 142k views

1 Answer

Mythic · Answer 1 · 2019-09-30T16:22:53+0000

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

$x = 39^\circ+2y$

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
$17^\circ$ .