Question

1. what formula does the video give for each exterior angle of a regular n - sided polygon?

a. $180\div n$ $180 - n$
b. $360\div n$ $360\div n$
c. $180\times(n - 2)$ $180\times(n - 2)$
d. $360\times(n - 2)$ $360\times(n - 2)$

1. what is the measure of each exterior angle for a regular pentagon ($n = 5$) as found in the video?

a. 45 45 degrees
b. 60 60 degrees
c. 72 72 degrees
d. 90 90 degrees

1. for a regular hexagon ($n = 6$), what did the video state is the measure of each interior angle?

a. 108 108 degrees
b. 120 120 degrees
c. 135 135 degrees
d. 150 150 degrees

1. for a regular octagon ($n = 8$), what is the measure of each interior angle according to the video?

a. 120 120 degrees
b. 135 135 degrees
c. 144 144 degrees
d. 160 160 degrees

1. why does the video say the sum of all exterior angles of any polygon equals 360 360 degrees?

a. because each interior angle equals 360 360 divided by $n$
b. because the exterior angles form arcs that together make a full circle of 360 360
c. because $180\times(n - 2)=360$ $180\times(n - 2)=360$ for all $n$
d. because interior and exterior angles are equal in measure

Explanation:

Question 6

For a regular \( n \)-sided polygon, the sum of all exterior angles is always \( 360^\circ \). To find each exterior angle, we divide the total sum of exterior angles (\( 360^\circ \)) by the number of sides (\( n \)). So the formula for each exterior angle is \( \frac{360}{n} \), which corresponds to option B.

Step 1: Recall the formula for exterior angle

We know from question 6 that the formula for each exterior angle of a regular \( n \)-sided polygon is \( \frac{360}{n} \).

Step 2: Substitute \( n = 5 \)

For a regular pentagon, \( n = 5 \). So we calculate \( \frac{360}{5}=72 \) degrees.

Step 1: Recall the formula for interior angle

The formula for each interior angle of a regular \( n \)-sided polygon is \( 180-\frac{360}{n} \) (since interior and exterior angles are supplementary) or alternatively, using the sum of interior angles formula \( (n - 2)\times180 \) and then dividing by \( n \), i.e., \( \frac{(n - 2)\times180}{n} \).

Step 2: Substitute \( n = 6 \)

For a regular hexagon, \( n = 6 \). Using the formula \( \frac{(n - 2)\times180}{n} \), we have \( \frac{(6 - 2)\times180}{6}=\frac{4\times180}{6}=\frac{720}{6} = 120 \) degrees.

Answer:

B. \( 360 \div n \)

Question 7