How large is an angle whose supplement is three times its complement?

i have a similar problem and its : an angle is 3 times its supplement. find the measure of the angle and the answer is: 135

how to solve it:
a = angle
A+ supplement = 180
A = 3(180 - A)
A = 540 - 3A
+3 + 3
4A = 540
___ ____
4 4

A = 135 deg.

The answer for the angle whose supplement is three times its complement is 67.5

To solve this problem, we need to understand the relationships between angles and their supplements and complements.

1. The supplement of an angle is the angle that, when added to the given angle, yields a sum of 180 degrees. Two angles are supplements of each other if their sum is equal to 180 degrees.

2. The complement of an angle is the angle that, when added to the given angle, yields a sum of 90 degrees. Two angles are complements of each other if their sum is equal to 90 degrees.

Let's solve this step by step:

Let's assume the measure of the angle is x degrees.

1. The supplement of this angle would be 180 - x degrees. (Remember, the sum of an angle and its supplement is 180 degrees.)
2. The complement of this angle would be 90 - x degrees. (The sum of an angle and its complement is 90 degrees.)

Given that the supplement of the angle is three times its complement, we can write the equation:

180 - x = 3(90 - x)

Now, let's solve for x:

180 - x = 270 - 3x // Distribute 3 to both terms
2x = 90 // Combine like terms
x = 45 // Divide both sides by 2

Therefore, the angle is 45 degrees.