The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. The smallest angle is

Options

A. 72°
B. 144°
C. 36°
D. 18°

Answer

To solve the problem of finding the smallest angle of a quadrilateral whose angles are in the ratio 1:2:3:4, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Total Sum of Angles in a Quadrilateral**:
The sum of all angles in a quadrilateral is always 360 degrees.

2. **Set Up the Ratio**:
Let the angles of the quadrilateral be represented as:
- First angle = \(1x\)
- Second angle = \(2x\)
- Third angle = \(3x\)
- Fourth angle = \(4x\)

3. **Write the Equation**:
According to the problem, the sum of these angles can be expressed as:
\[ 1x + 2x + 3x + 4x = 360 \]

4. **Combine Like Terms**:
Combine the terms on the left side:
\[ 10x = 360 \]

5. **Solve for x**:
To find the value of \(x\), divide both sides by 10:
\[ x = \frac{360}{10} = 36 \]

6. **Determine the Angles**:
Now that we have \(x\), we can find each angle:
- First angle = \(1x = 36\) degrees
- Second angle = \(2x = 2 \times 36 = 72\) degrees
- Third angle = \(3x = 3 \times 36 = 108\) degrees
- Fourth angle = \(4x = 4 \times 36 = 144\) degrees

7. **Identify the Smallest Angle**:
The smallest angle among these is:
\[ 36 \text{ degrees} \]

### Final Answer:
The smallest angle of the quadrilateral is **36 degrees**.

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