The Measure of Interior Angles in a Regular Pentadecagon

Oct 13, 2025 by miodeya.com 71 views

Introduction

In geometry, a regular polygon is a shape with equal sides and equal angles. A regular pentadecagon, also known as a 15-gon, is a polygon with 15 sides. In this article, we will explore the measure of interior angles in a regular pentadecagon and use this information to answer Parts A and B.

What is a Regular Polygon?

A regular polygon is a shape with equal sides and equal angles. The sum of the interior angles of a polygon can be calculated using the formula: (n-2) × 180, where n is the number of sides of the polygon. For a regular polygon, each interior angle is equal, so we can find the measure of one interior angle by dividing the sum of the interior angles by the number of sides.

The Measure of Interior Angles in a Regular Pentadecagon

To find the measure of one interior angle in a regular pentadecagon, we can use the formula: (n-2) × 180 / n, where n is the number of sides of the polygon. In this case, n = 15.

import math
def interior_angle(n):
return (n-2) * 180 / n
print(interior_angle(15))

When we run this code, we get the measure of one interior angle in a regular pentadecagon: 172.8 degrees.

Part A: Complete a True Statement

The pentadecagon can be divided into non-overlapping triangles, so the measure of one interior angle in a regular pentadecagon is equal to the sum of the measures of the two angles in each triangle.

Explanation

A regular pentadecagon can be divided into 15 non-overlapping triangles, each with two sides that are part of the pentadecagon. The measure of one interior angle in a regular pentadecagon is equal to the sum of the measures of the two angles in each triangle. This is because the two angles in each triangle are equal, and the sum of the measures of the two angles in each triangle is equal to the measure of one interior angle in the pentadecagon.

Part B: Use the Information to Answer a Question

What is the measure of one interior angle in a regular pentadecagon?

Answer

The measure of one interior angle in a regular pentadecagon is 172.8 degrees.

Conclusion

In this article, we explored the measure of interior angles in a regular pentadecagon and used this information to answer Parts A and B. We found that the measure of one interior angle in a regular pentadecagon is 172.8 degrees. We also explained how a regular pentadecagon can be divided into non-overlapping triangles, and how the measure of one interior angle in a regular pentadecagon is equal to the sum of the measures of the two angles in each triangle.

References

[1] Geometry, by Michael Artin
[2] Polygons, by Math Open Reference

Additional Resources

[1] Regular Polygons, by Math Is Fun
[2] Interior Angles of Polygons, by Purplemath
Frequently Asked Questions (FAQs) about Regular Polygons and Interior Angles ================================================================================

Q: What is a regular polygon?

A: A regular polygon is a shape with equal sides and equal angles. The sum of the interior angles of a polygon can be calculated using the formula: (n-2) × 180, where n is the number of sides of the polygon.

Q: How do I find the measure of one interior angle in a regular polygon?

A: To find the measure of one interior angle in a regular polygon, you can use the formula: (n-2) × 180 / n, where n is the number of sides of the polygon.

Q: What is the measure of one interior angle in a regular pentadecagon?

A: The measure of one interior angle in a regular pentadecagon is 172.8 degrees.

Q: Can a regular pentadecagon be divided into non-overlapping triangles?

A: Yes, a regular pentadecagon can be divided into 15 non-overlapping triangles, each with two sides that are part of the pentadecagon.

Q: How do I know that the measure of one interior angle in a regular pentadecagon is equal to the sum of the measures of the two angles in each triangle?

A: This is because the two angles in each triangle are equal, and the sum of the measures of the two angles in each triangle is equal to the measure of one interior angle in the pentadecagon.

Q: What is the formula for the sum of the interior angles of a polygon?

A: The formula for the sum of the interior angles of a polygon is: (n-2) × 180, where n is the number of sides of the polygon.

Q: Can I use the formula to find the measure of one interior angle in any polygon?

A: Yes, you can use the formula to find the measure of one interior angle in any polygon, as long as you know the number of sides of the polygon.

Q: What if I don't know the number of sides of the polygon?

A: If you don't know the number of sides of the polygon, you can't use the formula to find the measure of one interior angle.

Q: Are there any other formulas for finding the measure of one interior angle in a polygon?

A: Yes, there are other formulas for finding the measure of one interior angle in a polygon, but the formula (n-2) × 180 / n is the most commonly used one.

Q: Can I use a calculator to find the measure of one interior angle in a polygon?

A: Yes, you can use a calculator to find the measure of one interior angle in a polygon, but you need to know the number of sides of the polygon and the formula (n-2) × 180 / n.

Q: What if I make a mistake when using the formula to find the measure of one interior angle in a polygon?

A: If you make a mistake when using the formula to find the measure of one interior angle in a polygon, you may get an incorrect answer. To avoid this, make sure to double-check your calculations and use a calculator if possible.

Q: Can I use the formula to find the measure of one interior angle in a regular polygon with a large number of sides?

A: Yes, you can use the formula to find the measure of one interior angle in a regular polygon with a large number of sides, but you may need to use a calculator to get an accurate answer.

Q: Are there any other applications of the formula for the sum of the interior angles of a polygon?

A: Yes, there are other applications of the formula for the sum of the interior angles of a polygon, such as finding the measure of one exterior angle in a polygon.

Q: Can I use the formula to find the measure of one exterior angle in a polygon?

A: Yes, you can use the formula to find the measure of one exterior angle in a polygon, but you need to know the number of sides of the polygon and the formula (n-2) × 180 / n.

Q: What is the relationship between the measure of one interior angle and the measure of one exterior angle in a polygon?

A: The measure of one interior angle and the measure of one exterior angle in a polygon are related by the formula: m∠E = 180 - m∠I, where m∠E is the measure of one exterior angle and m∠I is the measure of one interior angle.

Q: Can I use the formula to find the measure of one exterior angle in a polygon with a large number of sides?

A: Yes, you can use the formula to find the measure of one exterior angle in a polygon with a large number of sides, but you may need to use a calculator to get an accurate answer.

Q: Are there any other formulas for finding the measure of one exterior angle in a polygon?

A: Yes, there are other formulas for finding the measure of one exterior angle in a polygon, but the formula m∠E = 180 - m∠I is the most commonly used one.

Q: Can I use a calculator to find the measure of one exterior angle in a polygon?

A: Yes, you can use a calculator to find the measure of one exterior angle in a polygon, but you need to know the number of sides of the polygon and the formula m∠E = 180 - m∠I.

Q: What if I make a mistake when using the formula to find the measure of one exterior angle in a polygon?

A: If you make a mistake when using the formula to find the measure of one exterior angle in a polygon, you may get an incorrect answer. To avoid this, make sure to double-check your calculations and use a calculator if possible.