A regular pentagon is simply a polygon whose all sides are same length and all angles are same measure. In order to find the measure of a each interior angle of a regular pentagon with 5 sides, we just divide the sum of the interior angles or (5-2) × 180 by the number of sides or 5. A regular pentagon sum of angle is 540°, and then each angle is `540/5` = 108°.
If polygons have n sides, the sum of its interior angles is 180° × (n-2).
An interior angle of a regular polygon with n sides is 180° × `(n-2)/n`
If you can measure the interior and exterior angle of straight line gives 180°. In all polygon figure interior angle is always supplementary to an exterior angle at that vertex is 180. Polygons Interior angles and exterior angles are complementary.
Tables for interior angles of regular polygon:
Sides |
Shape |
Sum of interior angles |
Each side angle |
3 |
Triangle |
180° |
60° |
4 |
Quadrilateral |
360° |
90° |
5 |
Pentagon |
540° |
108° |
6 |
Hexagon |
720° |
120° |
7 |
Heptagon |
900° |
128.57...° |
8 |
Octagon |
1080° |
135° |
“” |
“” |
“” |
“” |
n |
Any Polygon |
(n-2) × 180° |
(n-2) × 180° / n |
Problem 1:
What is the measure of interior angle in a regular pentagon?
Solution:
Sum of interior angles of a pentagon formula is = (n-2) × 180°
The regular pentagon has 5 sides.
Sum of interior angles of a pentagon is = (5 - 2) * 180°
= 3 * 180
= 540°
Therefore the sum of interior angles of a pentagon is 540°
Problem 2:
Find the each internal angle of pentagon.
Solution:
The regular pentagon has 5 sides.
Sum of interior angles of a pentagon is 540°
Formula:
An interior angle of a regular polygon with n sides is 180° × `(n-2)/n`
Equate the formula to 540 then find each angle
=180° × `(5-2)/5`
=180° * `3/5`
=`540/5`
=108°
Problem 3:
Find the sides of the pentagon. Pentagon each angle is 108 degrees.
Solution:
An interior angle of a regular polygon with n sides is 180° × `(n-2)/n`
So, 180° × (n-2) /n = 108
Multiply by n both sides.
180° × (n-2) = 108n
180n - 360 = 108n
Subtract both sides by 180n
-360 = -72n
Divide both sides by -72
5 = n
Therefore pentagon have 5 sides.