Which of the following can never be the measure of exterior angle of a regular polygon?

Options

A. `22°`
B. `36°`
C. `45°`
D. `30°`

Answer

To determine which of the given angles can never be the measure of an exterior angle of a regular polygon, we can use the property that the sum of all exterior angles of any polygon is always 360 degrees. The measure of each exterior angle of a regular polygon can be calculated using the formula:

\[ \text{Exterior Angle} = \frac{360}{n} \]

where \( n \) is the number of sides of the polygon. For an exterior angle to be valid, \( n \) must be a whole number.

### Step-by-Step Solution:

1. **Identify the given angles**: Let's assume the angles provided are 30°, 45°, 36°, and 22°.

2. **Calculate the number of sides for each angle**:
- For **30°**:
\[ n = \frac{360}{30} = 12 \]
This means a polygon with each exterior angle of 30° can have 12 sides (a dodecagon).

- For **45°**:
\[ n = \frac{360}{45} = 8 \]
This means a polygon with each exterior angle of 45° can have 8 sides (an octagon).

- For **36°**:
\[ n = \frac{360}{36} = 10 \]
This means a polygon with each exterior angle of 36° can have 10 sides (a decagon).

- For **22°**:
\[ n = \frac{360}{22} \approx 16.36 \]
This means a polygon with each exterior angle of 22° would require approximately 16.36 sides, which is not a whole number and therefore not possible.

3. **Conclusion**: Since the number of sides \( n \) must be a whole number, the angle that can never be the measure of an exterior angle of a regular polygon is **22°**.

### Final Answer:
The measure that can never be the exterior angle of a regular polygon is **22°**.