Question

1.5 triangles
score: 10.33/16 answered: 12/16
question 14
i can relate the sum of the interior angles with the numbers of sides given.
a) given a polygon with 8 sides, what is the sum of the interior angles?
what is the name of this polygon? select an answer
page 1
b) if the sum of the interior angles is 1800°, how many sides does it have?

Explanation:

Step1: Use the formula for the sum of interior angles

The formula for the sum of interior angles of a polygon is $(n - 2)\times180^{\circ}$, where $n$ is the number of sides.
For part a), $n = 8$.
$$(8 - 2)\times180^{\circ}=6\times180^{\circ}=1080^{\circ}$$
A polygon with 8 sides is called an octagon.

Step2: Solve for $n$ when the sum is given

For part b), set $(n - 2)\times180^{\circ}=1800^{\circ}$.
Divide both sides by $180^{\circ}$: $n - 2=\frac{1800^{\circ}}{180^{\circ}} = 10$.
Then add 2 to both sides: $n=10 + 2=12$.

Answer:

a) $1080^{\circ}$, octagon
b) $12$