Question

If all angles are measured in degrees, the ratio of three times the measure of $\angle A$ to four times the measure of the complement of $\angle A$ to half the measure of the supplement of $\angle A$ is $3:14:4$. What is the number of degrees in the measure of the complement of $\angle A$?

Answer 1

The measure of the complement of angle A is
`70\°`

Step-by-step explanation:

we know that

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

If two angles are supplementary, then their sum is equal to 180 degrees

Let

x ----> the measure of angle A

(90-x) ----> the measure of the complement of angle A

(180-x) ---> the measure of the supplement of angle A

we know that

`(3x)/(4(90-x))=(3)/(14)` -----> equation A

`(3x)/(0.5(180-x))=(3)/(4)` ----> equation B

Solve equation A or equation B to determine the value of x

Solve equation A

`(3x)/(4(x-90))=(3)/(14)`

`14(3x)=4(90-x)(3)\\42x=1,080-12x\\54x=1,080\\x=20`

Verify the value of x in the equation B

`(3(20))/(0.5(180-20))=(3)/(4)`

`(60)/(80)=(3)/(4)`

`(3)/(4)=(3)/(4)` ---> is ok

Find out the measure of the complement of angle A

(
`90-x)\°=(90-20)\°=70\°`