205k views
1 vote
NO LINKS!! URGENT HELP PLEASE!!

1. Find the sum of measures of the interior angles of the indicated polygons.

a. Hexagon

b. 23-gon

2. The sum of the measures of the interior angles of a convex polygon is 1440. Classify the polygon by the number of sides.

3. Find the sum of the measures of the exterior angles of a 32-gon.

User Itminus
by
9.6k points

2 Answers

4 votes

Answer:

a. (6 - 2) × 180 = 4 × 180 = 720 degrees.

b. (23 - 2) × 180 = 21 × 180 = 3780 degrees.

2. (n - 2) × 180 = 1440

n - 2 = 8

n = 10

3. 32 × (360/32) = 32 × 11.25 = 360 degrees.

User Emiliano Poggi
by
8.8k points
2 votes

Answer:

1.

a. 720 degrees.

b. 3780 degrees.

2. decagon

3. 360 degrees

Explanation:

1.

a. The sum of the measures of the interior angles of a hexagon can be found using the formula:

Sum of interior angles = (n-2) x 180 degrees

where n is the number of sides of the polygon. For a hexagon, n = 6, so we have:

Sum of interior angles = (6-2) x 180 degrees = 4 x 180 degrees = 720 degrees

Therefore, the sum of the measures of the interior angles of a hexagon is 720 degrees.

b. The sum of the measures of the interior angles of a 23-gon can be found using the same formula:

Sum of interior angles = (n-2) x 180 degrees

where n is the number of sides of the polygon. For a 23-gon, n = 23, so we have:

Sum of interior angles = (23-2) x 180 degrees = 21 x 180 degrees = 3780 degrees

Therefore, the sum of the measures of the interior angles of a 23-gon is 3780 degrees.

2.

The sum of the measures of the interior angles of a convex polygon with n sides can be found using the formula:

Sum of interior angles = (n-2) x 180 degrees

We are given that the sum of the measures of the interior angles is 1440 degrees. Substituting this value into the formula, we have:

1440 = (n-2) x 180 degrees

Simplifying and solving for n, we get:

n-2 = 1440/180 = 8

n = 8+2 = 10

Therefore, the polygon has 10 sides, and it is a decagon.

3.

The sum of the measures of the exterior angles of any polygon is always 360 degrees.

For a polygon with 32 sides, the sum of the exterior angles can be found using the same formula:

Sum of exterior angles = 360 degrees

Divided by the number of sides in the polygon, which is 32:

Sum of exterior angles = 360 degrees / 32 = 11.25 degrees

Therefore, the sum of the measures of the exterior angles of a 32-gon is 360 degrees, and each exterior angle of a regular 32-gon measures 11.25 degrees.

User ZearaeZ
by
8.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories