Complimentary and Supplementary Angles:
To understand the given problem, we first need to understand two types of angles: complimentary angles and supplementary angles.

1. Complimentary angles: Two angles are said to be complimentary if the sum of their measures is 90 degrees. In other words, if angle A + angle B = 90 degrees, then angles A and B are complimentary.

2. Supplementary angles: Two angles are said to be supplementary if the sum of their measures is 180 degrees. In other words, if angle A + angle B = 180 degrees, then angles A and B are supplementary.

The Problem:
The problem states that the compliment of an angle is one-third of its supplement. Let's assume the angle as x degrees.

Step 1: Find the Complement:
The complement of an angle is the difference between 90 degrees and the angle itself. So, the complement of angle x can be represented as (90 - x) degrees.

Step 2: Find the Supplement:
The supplement of an angle is the difference between 180 degrees and the angle itself. So, the supplement of angle x can be represented as (180 - x) degrees.

Step 3: Formulate the Equation:
According to the problem, the complement of angle x is one-third of its supplement. Mathematically, this can be represented as:
(90 - x) = (1/3)(180 - x)

Step 4: Solve the Equation:
To solve for x, we need to simplify the equation.
Multiply both sides of the equation by 3 to eliminate the fraction:
3(90 - x) = 180 - x

Simplify the equation:
270 - 3x = 180 - x

Combine like terms:
-3x + x = 180 - 270
-2x = -90

Divide both sides of the equation by -2:
x = -90 / -2
x = 45

The Solution:
The angle is 45 degrees.

Explanation:
When we substitute x = 45 in the equation, we get:
(90 - x) = (1/3)(180 - x)
(90 - 45) = (1/3)(180 - 45)
45 = (1/3)(135)

45 = 45

Hence, the angle is 45 degrees, which satisfies the given condition.