The given polygon will have 10 sides in total.
Given information:
The diagram shows part of a regular polygon. The sides of this polygon subtend angles of 36° at the center of the polygon.
Let the polygon has n number of sides. Now, the polygon is regular. So, its each side will be equal and it will make equal angle with the center.
The sum of angles made by all the sides will be equal to 360 degrees. So, the number of sides n can be calculated as,
36 x n = 360
n = 360/36
n = 10
Therefore the polygon will have 10 sides in total.