A pentagon has actually 5 sides, and also can be 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 to 3 × 180° = 540°

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

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

The internal Angles that a Pentagon add up to 540°

The general Rule

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


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

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

So the general ascendancy is:


Sum of inner Angles = (n−2) × 180°

Each angle (of a continual Polygon) = (n−2) × 180° / n


Perhaps an example will help:


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

*


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

And for a consistent Decagon:

Each inner angle = 1440°/10 = 144°


Note: interior Angles room sometimes dubbed "Internal Angles"


internal Angles Exterior Angles degrees (Angle) 2D shapes Triangles quadrilateral Geometry Index