Question

A regular polygon has 15 sides. Which is a possible angle of rotational symmetry for the figure?

Answer 1

Answer with explanation:

Number of sides of Regular Polygon = 15

Sum of Interior angles of Regular Polygon = (n-2)×180°

Sum of Interior angles of Regular Polygon having 15 Sides= (15-2)×180°

          =13 × 180°

           = 2340°

As, Each interior angle of Regular Polygon is equal.

Measure of each Interior angle

      $=\frac{2340}{15}\\\\=156$

     =156°

Measure of each Exterior angle = 180° -156°=24°

Angle of Rotational Symmetry of Polygon having 15 Sides=24°,48°,....=24°×n, Where ,n=1,2,3,....

→→You can find exterior angle by this method also.

Sum of exterior angles of any Polygon =360°

Measure of each interior angle of Regular polygon having 15 Sides

         $=\frac{360}{15}\\\\=24{\text{Degree}}$