Question

find the measure of the central angle of a regular polygon with 18 sides

Answer 1

i assume you are talking about a regular 18-gon with equal sides and equal angles. There will be 18 central angles forming triangles with the 18 sides. These central angles will add up to 360 degrees. Dividing 360 by 18, you find that each angle measures 20 degrees. 

Answer 2

The measure of the central angle of a regular polygon which has 18  number of sides is 20 degrees.

What is center angle of regular polygon?

A regular polygon is the polygon, whose all the sides and and angles are equal.

The central angle of f regular polygon is the angle made between the two consecutive vertex point from the center of the polygon.

The sum of all the central angles of a polygon is equal to the 360 degrees.

Therefore the central angle of regular polygon is ratio of 360 to the number of sides. It can be given as,

$C_a=\dfrac{360}{n}$

Here, (n) is the number of sides of a regular polygon.

In the given problem the polygon given has total number of sides is 18. Thus the central angle of this polygon with 18 sides, is find out using the above formula. Thus,

$C_a=\dfrac{360}{18}\\C_a=20^o$

Thus, the measure of the central angle of a regular polygon which has 18  number of sides is 20 degrees.

Learn more about the center angle of regular polygon here;

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