Regular Pentagon Angles

Polygons are the plane figure which is enclosed by its sides. Polygons are basically classified into two types. They are regular and irregular polygons. When all the sides of the polygon and the angles of the polygons are equal, then the polygon is said to be regular polygon. When the angles and sides of the polygons are different, then it is said to be irregular polygon. Pentagon is a polygon which possesses five sides. A regular pentagon has all its sides and angles are equal. In this article, we shall learn about the angle measures of regular pentagon.

 

Angles of a Regular Pentagon:

 

  Normally, the angles of pentagon are classified into two types.

  • Interior angle of a regular pentagon
  • Exterior angle of  a regular pentagon

These are the types of angles of a regular pentagon.

Interior angles of a regular pentagon:

  The interior angles of any polygon can be determined by using the formula,

        `(180(n)-360)/n`

   where n is the number of sides of the polygon

   Number of sides for a regular pentagon is 5.

   The interior angles of a regular pentagon can be obtained by substituting n = 5 in the formula. 

                        = `(180(5)-360)/5`

                        = `(900-360)/5`

                        = `540/5`

                        = 108°

interior angle of pentagon

Therefore the interior angle of a regular pentagon is 108°.

 

Sum of Interior angles fo a Regular Pentagon:

 

 The sum of interior angles of a regular pentagon is determined by using the formula,

              (n - 2)*180°

     where n is the number of sides of a polygon

   For pentagon, n = 5

    Substitute n = 5 in the formula to determine the sum of interior angles of a regular pentagon.

            = (5 - 2) * 180°

            = 3 * 180°

            = 540°

sum of interior angle of pentagon

Therefore the sum of interior angles of a regular pentagon is 540°.

 

Exterior angles of a Regular Pentagon:

   The exterior angle of any polygon can be determined by using the formula

           180° - interior angle

   The interior angle of a regular pentagon is 108°

   The exterior angles of a regular pentagon = 180 -108

                                                               = 72°

exterior angle of a pentagon

Therefore the exterior angles of a regular pentagon is 72°