exercises
find the sum of the measures of the interior angles of each convex polygon.
1. decagon
2. 16 - gon
3. 30 - gon
4. octagon
5. 12 - gon
6. 35 - gon

Question

Accepted Answer

### Problem 1: Decagon
# Explanation:
## Step1: Recall the formula for the sum of interior angles of a polygon.
The formula for the sum of the interior angles of a convex polygon with $ n $ sides is $ S=(n - 2)\times180^{\circ} $. A decagon has $ n = 10 $ sides.
## Step2: Substitute $ n = 10 $ into the formula.
$ S=(10 - 2)\times180^{\circ}=8\times180^{\circ} $
## Step3: Calculate the result.
$ 8\times180^{\circ}=1440^{\circ} $
# Answer: $ 1440^{\circ} $

### Problem 2: 16 - gon
# Explanation:
## Step1: Use the polygon interior angle sum formula $ S=(n - 2)\times180^{\circ} $, where $ n = 16 $.
## Step2: Substitute $ n = 16 $ into the formula.
$ S=(16 - 2)\times180^{\circ}=14\times180^{\circ} $
## Step3: Compute the value.
$ 14\times180^{\circ}=2520^{\circ} $
# Answer: $ 2520^{\circ} $

### Problem 3: 30 - gon
# Explanation:
## Step1: Apply the formula $ S=(n - 2)\times180^{\circ} $ with $ n = 30 $.
## Step2: Substitute $ n = 30 $ into the formula.
$ S=(30 - 2)\times180^{\circ}=28\times180^{\circ} $
## Step3: Calculate the product.
$ 28\times180^{\circ}=5040^{\circ} $
# Answer: $ 5040^{\circ} $

### Problem 4: Octagon
# Explanation:
## Step1: Recall the formula $ S=(n - 2)\times180^{\circ} $. An octagon has $ n = 8 $ sides.
## Step2: Substitute $ n = 8 $ into the formula.
$ S=(8 - 2)\times180^{\circ}=6\times180^{\circ} $
## Step3: Find the result.
$ 6\times180^{\circ}=1080^{\circ} $
# Answer: $ 1080^{\circ} $

### Problem 5: 12 - gon
# Explanation:
## Step1: Use the formula $ S=(n - 2)\times180^{\circ} $, where $ n = 12 $.
## Step2: Substitute $ n = 12 $ into the formula.
$ S=(12 - 2)\times180^{\circ}=10\times180^{\circ} $
## Step3: Calculate the value.
$ 10\times180^{\circ}=1800^{\circ} $
# Answer: $ 1800^{\circ} $

### Problem 6: 35 - gon
# Explanation:
## Step1: Apply the formula $ S=(n - 2)\times180^{\circ} $ with $ n = 35 $.
## Step2: Substitute $ n = 35 $ into the formula.
$ S=(35 - 2)\times180^{\circ}=33\times180^{\circ} $
## Step3: Compute the product.
$ 33\times180^{\circ}=5940^{\circ} $
# Answer: $ 5940^{\circ} $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: Decagon

Step1: Recall the formula for the sum of interior angles of a polygon.

Step2: Substitute \( n = 10 \) into the formula.

Step3: Calculate the result.

Step1: Use the polygon interior angle sum formula \( S=(n - 2)\times180^{\circ} \), where \( n = 16 \).

Step2: Substitute \( n = 16 \) into the formula.

Step3: Compute the value.

Step1: Apply the formula \( S=(n - 2)\times180^{\circ} \) with \( n = 30 \).

Step2: Substitute \( n = 30 \) into the formula.

Step3: Calculate the product.

Answer:

Problem 2: 16 - gon