Let the required angle be xTherefore, the supplement of the angle is x/3According to the question : x + x/3 = 180Sol.=> (3x + x)/3 = 180=> 4x = 180 *3 => 4x = 540 => x = 540/4Hence, x = 135The supplement = x/3 = 135/3 =》 45

The Angle and Its Supplement

Supplementary angles are a pair of angles that add up to 180 degrees. In this case, we are given that the supplementary angle of an angle is one third of the angle. Let's denote the given angle as "x".

Finding the Supplementary Angle:
To find the supplementary angle of "x", we can use the fact that supplementary angles add up to 180 degrees. Therefore, the supplementary angle can be represented as 180 - x.

Given Relationship:
According to the problem, the supplementary angle is one third of the given angle. Mathematically, this can be expressed as:

180 - x = (1/3)x

Solving the Equation:
To solve this equation, we can start by simplifying it. Multiplying both sides of the equation by 3, we have:

540 - 3x = x

Now, let's move all the "x" terms to one side of the equation:

540 = 4x

Dividing both sides of the equation by 4, we get:

x = 135

Identifying the Angle and Its Supplement:
Now that we have found the value of "x" to be 135 degrees, we can determine the angle and its supplement:

- The angle is "x", which is 135 degrees.
- The supplement of the angle is 180 - x, which is 180 - 135 = 45 degrees.

Explanation:
Based on the given information and the relationship between supplementary angles, we set up an equation to solve for the angle. By solving the equation, we found that the angle "x" is 135 degrees. Using the definition of supplementary angles, we determined that the supplement of this angle is 45 degrees.

Summary:
The angle is 135 degrees, and its supplement is 45 degrees. The angle and its supplement satisfy the condition that the supplement is one third of the angle, as stated in the problem.