Question

1. what is the sum of the interior angles of a 300 - sided polygon?
2. a polygon has interior angles that add up to 1980°. how many sides does it have?

180×11 = 1980°
it would have
11 sides

1. find the measure of one angle of an 8 - sided polygon.

Explanation:

Step1: Recall the formula for sum of interior angles

The formula for the sum of interior - angles of a polygon is $S=(n - 2)\times180^{\circ}$, where $n$ is the number of sides of the polygon.

Step2: Solve for the sum of interior angles of a 300 - sided polygon

For a 300 - sided polygon, $n = 300$. Substitute $n$ into the formula: $S=(300 - 2)\times180^{\circ}=298\times180^{\circ}=53640^{\circ}$.

Step3: Solve for the number of sides of a polygon with sum of interior angles 1980°

Given $S = 1980^{\circ}$, use the formula $S=(n - 2)\times180^{\circ}$. Then $1980=(n - 2)\times180$. Divide both sides by 180: $\frac{1980}{180}=n - 2$. So $11=n - 2$. Add 2 to both sides: $n=13$.

Step4: Solve for the measure of one angle of an 8 - sided polygon

First, find the sum of interior angles of an 8 - sided polygon. Using the formula $S=(n - 2)\times180^{\circ}$ with $n = 8$, we get $S=(8 - 2)\times180^{\circ}=6\times180^{\circ}=1080^{\circ}$. Since a regular 8 - sided polygon (octagon) has all angles equal, the measure of one angle is $\frac{1080^{\circ}}{8}=135^{\circ}$.

Answer:

1. The sum of the interior angles of a 300 - sided polygon is $53640^{\circ}$.
2. The polygon with interior angles adding up to $1980^{\circ}$ has 13 sides.
3. The measure of one angle of an 8 - sided polygon is $135^{\circ}$.