An angles measure is 3 times of its complement. find the measure of the angle and the measure of its complement.

Let the angle be Ø

then its complement is 90-Ø

Ø = 3(90-Ø)
Ø = 270 - 3Ø
4Ø = 270
Ø = 67.5

So the angle is 67.5° and its complement is 22.5°

To find the measure of the angle and its complement, let's first define the angle as x.

We know that the sum of an angle and its complement is always 90 degrees. So we can write the equation:

x + complement = 90

We are also given that the measure of the angle is 3 times its complement:

x = 3(complement)

Now we can substitute the value of x in the first equation:

3(complement) + complement = 90

Simplifying this equation, we get:

4(complement) = 90

To solve for the complement, we divide both sides of the equation by 4:

complement = 90/4

complement = 22.5 degrees

Now, we can substitute the value of the complement into the equation for the angle:

x = 3(22.5)

x = 67.5 degrees

Therefore, the measure of the angle is 67.5 degrees and the measure of its complement is 22.5 degrees.