Question

Each value of n represents the number of sides of a regular polygon. Determine whether the given angle measure is the correct sum of the interior angles of the polygon. Answer with 'Yes' or 'No'

n = 7; 868
n = 8; 1080
n = 9; 1260
n = 10; 1440

Answer 1

Explanation:

1.Yes

2.Yes

3.Yes

4.Yes

Answer 2

n = 7; 868 degrees - No

n = 8; 1080 degrees - Yes

n = 9; 1260 degrees - Yes

n = 10; 1440 degrees - Yes

Explanation:

To determine whether the given angle measures are the correct sums of the interior angles of the polygons, we can use the formula for finding the sum of the interior angles of a regular polygon:

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

Let's calculate the sum of the interior angles for each value of n and compare it to the given angle measure:

For n = 7:

Sum of interior angles = (7 - 2) * 180 = 5 * 180 = 900 degrees

Given angle measure = 868 degrees

Since the given angle measure (868 degrees) is less than the calculated sum of the interior angles (900 degrees), the answer is 'No'.

For n = 8:

Sum of interior angles = (8 - 2) * 180 = 6 * 180 = 1080 degrees

Given angle measure = 1080 degrees

Since the given angle measure (1080 degrees) is equal to the calculated sum of the interior angles (1080 degrees), the answer is 'Yes'.

For n = 9:

Sum of interior angles = (9 - 2) * 180 = 7 * 180 = 1260 degrees

Given angle measure = 1260 degrees

Since the given angle measure (1260 degrees) is equal to the calculated sum of the interior angles (1260 degrees), the answer is 'Yes'.

For n = 10:

Sum of interior angles = (10 - 2) * 180 = 8 * 180 = 1440 degrees

Given angle measure = 1440 degrees

Since the given angle measure (1440 degrees) is equal to the calculated sum of the interior angles (1440 degrees), the answer is 'Yes'.

In summary:

n = 7; 868 degrees - No

n = 8; 1080 degrees - Yes

n = 9; 1260 degrees - Yes

n = 10; 1440 degrees - Yes