Question

The polygon is a regular nonagon (9-sides). What is the sum of the interior angles? What is the measurement for each angle?

Answer 1

Divide the nonagon radially into 9 congruent, equilateral isosceles triangle. Each triangle has vertex angle of 360°/9 = 40°.
Interior angle of polygon = 180°-40° = 140°.
Sum of interior angles = 9(140°) = 1260°

Answer 2

To solve the problem we will first calculate the sum of all the interior angles.

What is the sum of all the interior angles of the n numbered polygon?

The sum of all the interior angles of n numbered polygon is given as,

the sum of all the interior angles of n numbered polygon = (n-2) x 180°.

Given to us

• Number of sides = 9 sides,

A.)  the sum of the interior angles,

Sum of the interior angles,

the sum of the interior angles = (n-2) x 180°

                                                   = (9-2) x 180°

                                                   = (7) x 180°

                                                   = 1,260°

Thus, the measurement of the sum of the interior angles of a 9 sided polygon is 1260°.

B.) the measurement for each angle

The measurement for each angle

$\text{Measurement for each angle} = \dfrac{\text{sum of all the interior angles}}{\text{Number of sides}}$

$\text{Measurement for each angle} = \dfrac{1260^o}{9}$

                                            $= 140^o$

Hence, the measurement of each angle of a 9 sided polygon is 140°.

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