Find the angle whose supplement is four times its complement.

Options

A. `30^(@)`
B. `45^(@`
C. `60^(@)`
D. `90^(@)`

Explanation

To find the angle whose supplement is four times its complement, we can follow these steps:

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

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

### Step 3: Set up the equation based on the problem statement
According to the question, the supplement is four times the complement. Therefore, we can write the equation as:
\[ 180^\circ - \theta = 4(90^\circ - \theta) \]

### Step 4: Expand and simplify the equation
Expanding the right side of the equation:
\[ 180^\circ - \theta = 360^\circ - 4\theta \]

Now, rearranging the equation to isolate \( \theta \):
\[ 180^\circ - \theta + 4\theta = 360^\circ \]
\[ 180^\circ + 3\theta = 360^\circ \]

### Step 5: Solve for \( \theta \)
Subtract \( 180^\circ \) from both sides:
\[ 3\theta = 360^\circ - 180^\circ \]
\[ 3\theta = 180^\circ \]

Now, divide both sides by 3:
\[ \theta = \frac{180^\circ}{3} \]
\[ \theta = 60^\circ \]

### Step 6: Conclusion
The angle whose supplement is four times its complement is:
\[ \theta = 60^\circ \]

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