Answer :

Sure, let's solve the problem step-by-step for each part:

### Finding the Number of Sides of a Regular Polygon for Given Exterior Angles:

a) Exterior Angle: 24°

For any regular polygon, the sum of the exterior angles always equals 360°. To find the number of sides ([tex]\( n \)[/tex]), we can use the formula:
[tex]\[ n = \frac{360^\circ}{\text{Exterior Angle}} \][/tex]

For an exterior angle of 24°:
[tex]\[ n = \frac{360^\circ}{24^\circ} = 15 \][/tex]

So, the polygon has 15 sides.

b) Exterior Angle: 60°

Using the same formula:

For an exterior angle of 60°:
[tex]\[ n = \frac{360^\circ}{60^\circ} = 6 \][/tex]

So, the polygon has 6 sides.

### Finding the Size of Each Interior Angle for Given Exterior Angles:

The interior angle ([tex]\(\text{Interior Angle}\)[/tex]) of a regular polygon can be found using the relationship:
[tex]\[ \text{Interior Angle} = 180^\circ - \text{Exterior Angle} \][/tex]

c) Exterior Angle: 72°

For an exterior angle of 72°, the interior angle is:
[tex]\[ \text{Interior Angle} = 180^\circ - 72^\circ = 108^\circ \][/tex]

d) Exterior Angle: 120°

For an exterior angle of 120°, the interior angle is:
[tex]\[ \text{Interior Angle} = 180^\circ - 120^\circ = 60^\circ \][/tex]

### Summary of Answers:

- Number of sides:
- For exterior angle 24°: 15 sides
- For exterior angle 60°: 6 sides
- Interior angles:
- For exterior angle 72°: 108°
- For exterior angle 120°: 60°

To conclude, the number of sides and the corresponding interior angles for the given exterior angles are as follows:
- [tex]\(24^\circ\)[/tex] : 15 sides
- [tex]\(60^\circ\)[/tex] : 6 sides
- [tex]\(72^\circ\)[/tex] : [tex]\(\text{Interior Angle} = 108^\circ\)[/tex]
- [tex]\(120^\circ\)[/tex] : [tex]\(\text{Interior Angle} = 60^\circ\)[/tex]