If an angle is one-third of its supplement, then the measure of the angle is

Options

A. `45^(@)`
B. `30^(@)`
C. `135^(@)`
D. `150^(@)`

Answer

To solve the problem, we need to find the measure of an angle that is one-third of its supplement. Let's break it down step by step.

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

### Step 2: Understand the concept of supplementary angles
The supplement of an angle \( x \) is given by \( 180^\circ - x \). According to the problem, the angle \( x \) is one-third of its supplement. Therefore, we can write the equation:
\[ x = \frac{1}{3}(180^\circ - x) \]

### Step 3: Set up the equation
Now, we can multiply both sides of the equation by 3 to eliminate the fraction:
\[ 3x = 180^\circ - x \]

### Step 4: Combine like terms
Next, we will add \( x \) to both sides to combine the \( x \) terms:
\[ 3x + x = 180^\circ \]
This simplifies to:
\[ 4x = 180^\circ \]

### Step 5: Solve for \( x \)
Now, divide both sides by 4 to find the value of \( x \):
\[ x = \frac{180^\circ}{4} = 45^\circ \]

### Step 6: Conclusion
Thus, the measure of the angle is \( 45^\circ \).