Question

A regular polygon is drawn in a circle so that each vertex is on the circle and is connected to the center by a radius. each of the central angles has a measure of 40°. how many sides does the polygon have? 8 9 10 12

Answer 1

Answer:

9 is correct

Step-by-step explanation:

Edge 2021

Answer 2

The polygon will have $9$ sides.

What is polygon ?

Polygon is a two-dimensional geometric figure that has a finite number of sides.

We have,

A polygon inside a circle.

Measure of central angle of polygon $=40^0$

Number of sides of polygon $=n$

So,

Total angle of circle $=360^0$

Measure of central angle of polygon $=40^0$

i.e.

EACH central angle $= \frac{360}{Number\ of\ sides }$

i.e.

$40^0=\frac{360^0}{n}$

⇒ $n=\frac{360}{40}$

$n=9$

So, the polygon have $9$ number of sides.

Hence, we can say that the polygon have $9$ number of sides.

To know more about polygon click here

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