Question

An angle measured 10 degrees less than the measure of its complementary angle. Find the measure of both angles

Answer 1

The measure of the angles are 40 degrees and 50 degrees

Explanation:

Let

x ----> the measure of one angle in degrees

y ----> the measure of the complementary angle in degrees

we know that

If two angles are complementary, then their sum is equal to 90 degrees

so

`x+y=90` ----> equation A

we have that

`x=y-10` ----> equation B

Substitute equation B in equation A and solve for y

`(y-10)+y=90\\2y-10=90\\2y=100\\y=50`

Find the value of x

`x=50-10=40`

therefore

The measure of the angles are 40 degrees and 50 degrees