A pentagon has actually 5 sides, and also can be made native three triangles, so you understand what ...

You are watching: How many degrees are in each interior angle of a regular pentagon?

... Its inner angles add up come 3 × 180° = 540°

And when it is regular (all angles the same), then each angle is 540° / 5 = 108°

(Exercise: make certain each triangle right here adds as much as 180°, and also check the the pentagon"s inner angles add up come 540°)

The inner Angles the a Pentagon include up come 540°

The basic Rule

Each time we add a next (triangle come quadrilateral, quadrilateral to pentagon, etc), we add one more 180° to the total:


ShapeSidesSum ofInterior AnglesShapeEach Angle
If that is a Regular Polygon (all sides are equal, all angles are equal)
Triangle3180°
*
60°
Quadrilateral4360°
*
90°
Pentagon5540°
*
108°
Hexagon6720°
*
120°
Heptagon (or Septagon)7900°
*
128.57...°
Octagon81080°
*
135°
Nonagon91260°
*
140°
...........

See more: Middle School Math With Pizzazz Book A Th With Pizzazz Book A Pdf

...
Any Polygonn(n−2) × 180°
*
(n−2) × 180° / n

So the general rule is:


Sum of internal Angles = (n−2) × 180°

Each edge (of a continuous Polygon) = (n−2) × 180° / n


Perhaps an example will help:


Example: What about a continual Decagon (10 sides) ?

*


Sum of inner Angles = (n−2) × 180°
= (10−2) × 180°
= 8 × 180°
= 1440°

And for a regular Decagon:

Each inner angle = 1440°/10 = 144°


Note: inner Angles are sometimes called "Internal Angles"


interior Angles Exterior Angles degrees (Angle) 2D forms Triangles quadrilateral Geometry Index