Question

Aregular 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?
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Answer 1

The number of sides the polygon have 9

Explanation:

Given in question as :

For The circle , the central angles measure be 40 °

Let the number of sides of polygon = n

Now . as we know

External angle =
`(360^(\circ) )/(n)`

Or , 40° =
`(360^(\circ) )/(n)`

Or,
`(360^(\circ) )/(n)` = 40°

Or,
`(360^(\circ) )/(n)` = 40°

So, n =
`(360^(\circ) )/(40^(\circ))` = 9

Hence The number of sides the polygon have 9 Answer