Question

The measure of one angle is six more than half the measure of another angle. If the angles are complementary, find both measures?

Answer 1

34°, 56°

Explanation:

Let the angles be x and y. It is given that

x = 0.5y +6

Also,

Angles are complimentary which means:

x+y= 90°

Substitute value of x:

0.5y+6+y =90

Solve for y

1.5 y =84

y = 56°

So, x = 90-y = 90-56=34°

Answer 2

The measure of the angles are 34° and 56°

Explanation:

Let

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

y -----> the measure of another angle

we know that

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

so

x+y=90° -----> equation A

x=0.5y+6 ----> equation B

substitute equation B in equation A and solve for y

0.5y+6+y=90

1.5y=90-6

1.5y=84

y=56°

Find the value of x

x=0.5(56)+6=34°

therefore

The measure of the angles are 34° and 56°