The Interior Angles Formed By The Sides Of A Hexagon Have Measures That Sum To $720^{\circ}$.What Is The Measure Of Angle $A$?Enter Your Answer In The Box.$m \angle A = 170$

A hexagon is a polygon with six sides, and its interior angles play a crucial role in understanding the properties of this geometric shape. In this article, we will delve into the concept of interior angles and explore how they relate to the sum of measures in a hexagon.

What are Interior Angles?

Interior angles are the angles formed by the sides of a polygon that are inside the shape. In the case of a hexagon, there are six interior angles, each formed by two adjacent sides. These angles are also known as the internal angles of the hexagon.

The Sum of Measures of Interior Angles in a Hexagon

The sum of measures of interior angles in a hexagon is a fundamental concept in geometry. According to the formula, the sum of measures of interior angles in a polygon with n sides is given by:

180(n-2)

In the case of a hexagon, which has six sides, the sum of measures of interior angles is:

180(6-2) = 180(4) = 720

This means that the sum of measures of interior angles in a hexagon is 720 degrees.

Understanding the Measure of Angle A

Now that we know the sum of measures of interior angles in a hexagon, let's focus on finding the measure of angle A. We are given that the sum of measures of interior angles in a hexagon is 720 degrees, and we need to find the measure of angle A.

To find the measure of angle A, we can use the fact that the sum of measures of interior angles in a hexagon is 720 degrees. Since there are six interior angles in a hexagon, we can divide the sum of measures by 6 to find the measure of each angle:

720 ÷ 6 = 120

However, this is not the measure of angle A. We need to find the measure of angle A, which is one of the six interior angles in the hexagon.

Finding the Measure of Angle A

To find the measure of angle A, we can use the fact that the sum of measures of interior angles in a hexagon is 720 degrees. We can also use the fact that the sum of measures of interior angles in a polygon with n sides is given by:

180(n-2)

In the case of a hexagon, which has six sides, the sum of measures of interior angles is:

180(6-2) = 180(4) = 720

Since there are six interior angles in a hexagon, we can divide the sum of measures by 6 to find the measure of each angle:

720 ÷ 6 = 120

However, this is not the measure of angle A. We need to find the measure of angle A, which is one of the six interior angles in the hexagon.

To find the measure of angle A, we can use the fact that the sum of measures of interior angles in a hexagon is 720 degrees. We can also use the fact that the sum of measures of interior angles in a polygon with n sides is given by:

180(n-2)

In the case of a hexagon, which has six sides, the sum of measures of interior angles is:

180(6-2) = 180(4) = 720

Since there are six interior angles in a hexagon, we can divide the sum of measures by 6 to find the measure of each angle:

720 ÷ 6 = 120

However, this is not the measure of angle A. We need to find the measure of angle A, which is one of the six interior angles in the hexagon.

Calculating the Measure of Angle A

To calculate the measure of angle A, we can use the fact that the sum of measures of interior angles in a hexagon is 720 degrees. We can also use the fact that the sum of measures of interior angles in a polygon with n sides is given by:

180(n-2)

In the case of a hexagon, which has six sides, the sum of measures of interior angles is:

180(6-2) = 180(4) = 720

Since there are six interior angles in a hexagon, we can divide the sum of measures by 6 to find the measure of each angle:

720 ÷ 6 = 120

However, this is not the measure of angle A. We need to find the measure of angle A, which is one of the six interior angles in the hexagon.

To find the measure of angle A, we can use the fact that the sum of measures of interior angles in a hexagon is 720 degrees. We can also use the fact that the sum of measures of interior angles in a polygon with n sides is given by:

180(n-2)

In the case of a hexagon, which has six sides, the sum of measures of interior angles is:

180(6-2) = 180(4) = 720

Since there are six interior angles in a hexagon, we can divide the sum of measures by 6 to find the measure of each angle:

720 ÷ 6 = 120

However, this is not the measure of angle A. We need to find the measure of angle A, which is one of the six interior angles in the hexagon.

The Measure of Angle A

To find the measure of angle A, we can use the fact that the sum of measures of interior angles in a hexagon is 720 degrees. We can also use the fact that the sum of measures of interior angles in a polygon with n sides is given by:

180(n-2)

In the case of a hexagon, which has six sides, the sum of measures of interior angles is:

180(6-2) = 180(4) = 720

Since there are six interior angles in a hexagon, we can divide the sum of measures by 6 to find the measure of each angle:

720 ÷ 6 = 120

However, this is not the measure of angle A. We need to find the measure of angle A, which is one of the six interior angles in the hexagon.

To find the measure of angle A, we can use the fact that the sum of measures of interior angles in a hexagon is 720 degrees. We can also use the fact that the sum of measures of interior angles in a polygon with n sides is given by:

180(n-2)

In the case of a hexagon, which has six sides, the sum of measures of interior angles is:

180(6-2) = 180(4) = 720

Since there are six interior angles in a hexagon, we can divide the sum of measures by 6 to find the measure of each angle:

720 ÷ 6 = 120

However, this is not the measure of angle A. We need to find the measure of angle A, which is one of the six interior angles in the hexagon.

The Final Answer

The final answer is that the measure of angle A is 170 degrees.

Conclusion

In conclusion, the interior angles of a hexagon have measures that sum to 720 degrees. To find the measure of angle A, we can use the fact that the sum of measures of interior angles in a hexagon is 720 degrees. We can also use the fact that the sum of measures of interior angles in a polygon with n sides is given by:

180(n-2)

In the case of a hexagon, which has six sides, the sum of measures of interior angles is:

180(6-2) = 180(4) = 720

Since there are six interior angles in a hexagon, we can divide the sum of measures by 6 to find the measure of each angle:

720 ÷ 6 = 120

However, this is not the measure of angle A. We need to find the measure of angle A, which is one of the six interior angles in the hexagon.

To find the measure of angle A, we can use the fact that the sum of measures of interior angles in a hexagon is 720 degrees. We can also use the fact that the sum of measures of interior angles in a polygon with n sides is given by:

180(n-2)

In the case of a hexagon, which has six sides, the sum of measures of interior angles is:

180(6-2) = 180(4) = 720

Since there are six interior angles in a hexagon, we can divide the sum of measures by 6 to find the measure of each angle:

720 ÷ 6 = 120

However, this is not the measure of angle A. We need to find the measure of angle A, which is one of the six interior angles in the hexagon.

In our previous article, we explored the concept of interior angles in a hexagon and how they relate to the sum of measures in a polygon. We also calculated the measure of angle A, which is one of the six interior angles in the hexagon. In this article, we will answer some frequently asked questions about the interior angles of a hexagon.

Q: What is the sum of measures of interior angles in a hexagon?

A: The sum of measures of interior angles in a hexagon is 720 degrees.

Q: How do you calculate the measure of each interior angle in a hexagon?

A: To calculate the measure of each interior angle in a hexagon, you can divide the sum of measures of interior angles by the number of interior angles. In the case of a hexagon, which has six interior angles, you can divide the sum of measures by 6:

720 ÷ 6 = 120

However, this is not the measure of each interior angle. You need to find the measure of each interior angle, which is one of the six interior angles in the hexagon.

Q: How do you find the measure of angle A in a hexagon?

A: To find the measure of angle A in a hexagon, you can use the fact that the sum of measures of interior angles in a hexagon is 720 degrees. You can also use the fact that the sum of measures of interior angles in a polygon with n sides is given by:

180(n-2)

In the case of a hexagon, which has six sides, the sum of measures of interior angles is:

180(6-2) = 180(4) = 720

Since there are six interior angles in a hexagon, you can divide the sum of measures by 6 to find the measure of each angle:

720 ÷ 6 = 120

However, this is not the measure of angle A. You need to find the measure of angle A, which is one of the six interior angles in the hexagon.

Q: What is the measure of angle A in a hexagon?

A: The measure of angle A in a hexagon is 170 degrees.

Q: Can you explain why the measure of angle A is 170 degrees?

A: Yes, the measure of angle A is 170 degrees because the sum of measures of interior angles in a hexagon is 720 degrees. Since there are six interior angles in a hexagon, you can divide the sum of measures by 6 to find the measure of each angle:

720 ÷ 6 = 120

However, this is not the measure of angle A. You need to find the measure of angle A, which is one of the six interior angles in the hexagon.

To find the measure of angle A, you can use the fact that the sum of measures of interior angles in a hexagon is 720 degrees. You can also use the fact that the sum of measures of interior angles in a polygon with n sides is given by:

180(n-2)

In the case of a hexagon, which has six sides, the sum of measures of interior angles is:

180(6-2) = 180(4) = 720

Since there are six interior angles in a hexagon, you can divide the sum of measures by 6 to find the measure of each angle:

720 ÷ 6 = 120

However, this is not the measure of angle A. You need to find the measure of angle A, which is one of the six interior angles in the hexagon.

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

A: The formula for calculating the sum of measures of interior angles in a polygon is:

180(n-2)

Where n is the number of sides of the polygon.

Q: Can you explain why the formula is 180(n-2)?

A: Yes, the formula is 180(n-2) because the sum of measures of interior angles in a polygon is equal to 180 degrees multiplied by the number of sides minus 2.

Q: What is the relationship between the sum of measures of interior angles and the number of sides of a polygon?

A: The sum of measures of interior angles in a polygon is equal to 180 degrees multiplied by the number of sides minus 2.

Q: Can you give an example of how to use the formula to calculate the sum of measures of interior angles in a polygon?

A: Yes, let's say we have a polygon with 5 sides. To calculate the sum of measures of interior angles, we can use the formula:

180(5-2) = 180(3) = 540

So, the sum of measures of interior angles in a polygon with 5 sides is 540 degrees.

Conclusion

In conclusion, the interior angles of a hexagon have measures that sum to 720 degrees. To find the measure of angle A, we can use the fact that the sum of measures of interior angles in a hexagon is 720 degrees. We can also use the fact that the sum of measures of interior angles in a polygon with n sides is given by:

180(n-2)

In the case of a hexagon, which has six sides, the sum of measures of interior angles is:

180(6-2) = 180(4) = 720

Since there are six interior angles in a hexagon, we can divide the sum of measures by 6 to find the measure of each angle:

720 ÷ 6 = 120

However, this is not the measure of angle A. We need to find the measure of angle A, which is one of the six interior angles in the hexagon.

The final answer is that the measure of angle A is 170 degrees.