Question

directions - use the polygon angle sum theorem to find the sum of the interior angles:

number of sides =
sum of the interior angles =

number of sides =
sum of the interior angles =

number of sides =
sum of the interior angles =

Explanation:

Step1: Determine the number of sides for each polygon

• For the first polygon (left - most), it is a non - agon (9 - sided polygon). So, the number of sides \(n_1 = 9\).
• For the second polygon (middle), it is a hexagon. So, the number of sides \(n_2=6\).
• For the third polygon (right - most), it is a decagon (10 - sided polygon). So, the number of sides \(n_3 = 10\).

Step2: Use the polygon angle - sum formula \(S=(n - 2)\times180^{\circ}\)

• For \(n = 9\):

$$
LATEXBLOCK0
$$

• For \(n = 6\):

$$
LATEXBLOCK1
$$

• For \(n = 10\):

$$
LATEXBLOCK2
$$

Answer:

• First polygon: Number of sides \(=9\), Sum of the interior angles \(=1260^{\circ}\)
• Second polygon: Number of sides \(=6\), Sum of the interior angles \(=720^{\circ}\)
• Third polygon: Number of sides \(=10\), Sum of the interior angles \(=1440^{\circ}\)