Question

The measure of A is 4 degrees greater than the measure of B. The two angles are complementary. Find the measure of each angle

Answer 1

angle B =X angle A = x+4 complementary angles= 90 degrees x+x+4= 90 2x= 86 x= 43 degrees for angle B 43+4 = 47 degrees for angle A Hope this helps

Answer 2

Two angles are said to be complementary angles if the sum of the measure of angles is 90 degree.

As per the statement:

The measure of A is 4 degrees greater than the measure of B

⇒
`m \angle A = 4^(\circ) + m\angle B` .....[1]

It is given that: The two angles are complementary

By definition of complementary angles;

`m \angle A+ m\angle B = 90^(\circ)` .......[2]

Substitute equation [1] into [2] we have;

`4^(\circ) + m\angle B + m\angle B =90^(\circ)`

⇒
`4^(\circ) + 2 m\angle B =90^(\circ)`

Subtract 4 degree from both sides we have;

`2 m\angle B=86^(\circ)`

Divide both sides by 2 we have';

`m \angle B = 43`

Substitute in [1] we have;

`m \angle A = 4 + 43 = 47^(\circ)`

Therefore, measure of each angles are:

`m \angle A= 47` and
`m \angle B = 43`