A pentagon has actually 5 sides, and can it is in made native three triangles, therefore you recognize what ...

You are watching: What is the measure of each interior angle of a regular pentagon?

... Its interior angles include up come 3 × 180° = 540°

And as soon as it is regular (all angle the same), then each edge is 540° / 5 = 108°

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

The internal Angles of a Pentagon include up come 540°

The general Rule

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


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

See more: What Does The Name Traci Mean ? What Does Traci Mean

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

So the general ascendancy is:


Sum of interior Angles = (n−2) × 180°

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


Perhaps an example will help:


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

*


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

And for a consistent Decagon:

Each internal angle = 1440°/10 = 144°


Note: inner Angles room sometimes called "Internal Angles"


interior Angles Exterior Angles degrees (Angle) 2D shapes Triangles square Geometry Index