Possible Measures for Exterior Angles

Oct 13, 2025 by talynt.org 24 views

Determine which of the following are possible measures for the exterior angles of a regular polygon

A regular polygon is a shape with equal sides and equal angles. The sum of the exterior angles of any polygon is always 360°. In a regular polygon, all exterior angles are equal. To determine if a given measure is possible for the exterior angle of a regular polygon, we need to check if it can divide 360° evenly.

Possible Measures for Exterior Angles

Let's analyze each given measure to see if it's possible for the exterior angle of a regular polygon.

90°

The given measure of an exterior angle is 90°. To check if this is possible, we need to see if 90° can divide 360° evenly.

360° ÷ 90° = 4

Since 90° can divide 360° evenly, it is possible for the exterior angle of a regular polygon. A regular polygon with an exterior angle of 90° would have 4 sides.

80°

The given measure of an exterior angle is 80°. To check if this is possible, we need to see if 80° can divide 360° evenly.

360° ÷ 80° = 4.5

Since 80° cannot divide 360° evenly, it is not possible for the exterior angle of a regular polygon.

75°

The given measure of an exterior angle is 75°. To check if this is possible, we need to see if 75° can divide 360° evenly.

360° ÷ 75° = 4.8

Since 75° cannot divide 360° evenly, it is not possible for the exterior angle of a regular polygon.

30°

The given measure of an exterior angle is 30°. To check if this is possible, we need to see if 30° can divide 360° evenly.

360° ÷ 30° = 12

Since 30° can divide 360° evenly, it is possible for the exterior angle of a regular polygon. A regular polygon with an exterior angle of 30° would have 12 sides.

46°

The given measure of an exterior angle is 46°. To check if this is possible, we need to see if 46° can divide 360° evenly.

360° ÷ 46° = 7.87

Since 46° cannot divide 360° evenly, it is not possible for the exterior angle of a regular polygon.

36°

The given measure of an exterior angle is 36°. To check if this is possible, we need to see if 36° can divide 360° evenly.

360° ÷ 36° = 10

Since 36° can divide 360° evenly, it is possible for the exterior angle of a regular polygon. A regular polygon with an exterior angle of 36° would have 10 sides.

2°

The given measure of an exterior angle is 2°. To check if this is possible, we need to see if 2° can divide 360° evenly.

360° ÷ 2° = 180

Since 2° can divide 360° evenly, it is possible for the exterior angle of a regular polygon. A regular polygon with an exterior angle of 2° would have 180 sides.

In conclusion, the possible measures for the exterior angles of a regular polygon are 90° (4 sides), 30° (12 sides), 36° (10 sides), and 2° (180 sides). The other given measures, 80°, 75°, 46°, and 36°, are not possible for the exterior angle of a regular polygon.
Determine which of the following are possible measures for the exterior angles of a regular polygon: Q&A

In our previous article, we discussed how to determine if a given measure is possible for the exterior angle of a regular polygon. We analyzed each given measure to see if it can divide 360° evenly. In this article, we will provide a Q&A section to help you better understand the concept.

Q: What is the sum of the exterior angles of any polygon?

A: The sum of the exterior angles of any polygon is always 360°.

Q: What is a regular polygon?

A: A regular polygon is a shape with equal sides and equal angles.

Q: How do I determine if a given measure is possible for the exterior angle of a regular polygon?

A: To determine if a given measure is possible for the exterior angle of a regular polygon, you need to see if it can divide 360° evenly.

Q: What is the formula to check if a given measure is possible for the exterior angle of a regular polygon?

A: The formula is: 360° ÷ given measure = number of sides

Q: What if the result of the formula is not a whole number?

A: If the result of the formula is not a whole number, then the given measure is not possible for the exterior angle of a regular polygon.

Q: Can a regular polygon have an exterior angle of 90°?

A: Yes, a regular polygon can have an exterior angle of 90°. A regular polygon with an exterior angle of 90° would have 4 sides.

Q: Can a regular polygon have an exterior angle of 30°?

A: Yes, a regular polygon can have an exterior angle of 30°. A regular polygon with an exterior angle of 30° would have 12 sides.

Q: Can a regular polygon have an exterior angle of 2°?

A: Yes, a regular polygon can have an exterior angle of 2°. A regular polygon with an exterior angle of 2° would have 180 sides.

Q: Can a regular polygon have an exterior angle of 80°?

A: No, a regular polygon cannot have an exterior angle of 80°. 80° cannot divide 360° evenly.

Q: Can a regular polygon have an exterior angle of 75°?

A: No, a regular polygon cannot have an exterior angle of 75°. 75° cannot divide 360° evenly.

Q: Can a regular polygon have an exterior angle of 46°?

A: No, a regular polygon cannot have an exterior angle of 46°. 46° cannot divide 360° evenly.

Q: Can a regular polygon have an exterior angle of 36°?

A: Yes, a regular polygon can have an exterior angle of 36°. A regular polygon with an exterior angle of 36° would have 10 sides.

In conclusion, we hope this Q&A section has helped you better understand how to determine if a given measure is possible for the exterior angle of a regular polygon. Remember, the sum of the exterior angles of any polygon is always 360°, and a regular polygon has equal sides and equal angles.