Find the angle whose complement is one third of its supplement.

Explanation

To find the angle whose complement is one-third of its supplement, we can follow these steps:

### Step 1: Define the angle
Let the angle be \( x \).

### Step 2: Write the expressions for complement and supplement
- The complement of \( x \) is given by:
\[ \text{Complement} = 90^\circ - x \]
- The supplement of \( x \) is given by:
\[ \text{Supplement} = 180^\circ - x \]

### Step 3: Set up the equation
According to the problem, the complement is one-third of the supplement. Therefore, we can write the equation:
\[ 90^\circ - x = \frac{1}{3}(180^\circ - x) \]

### Step 4: Eliminate the fraction
To eliminate the fraction, multiply both sides of the equation by 3:
\[ 3(90^\circ - x) = 180^\circ - x \]

### Step 5: Distribute on the left side
Distributing the 3 on the left side gives:
\[ 270^\circ - 3x = 180^\circ - x \]

### Step 6: Rearrange the equation
Now, let's rearrange the equation to isolate \( x \):
1. Move \( 180^\circ \) to the left side:
\[ 270^\circ - 180^\circ = 3x - x \]
2. Simplifying this gives:
\[ 90^\circ = 2x \]

### Step 7: Solve for \( x \)
To find \( x \), divide both sides by 2:
\[ x = \frac{90^\circ}{2} = 45^\circ \]

### Final Answer
The angle whose complement is one-third of its supplement is:
\[ \boxed{45^\circ} \]

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