A pentagon has 5 sides, and can be made from three triangles, so you know what ...

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

... its interior angles add up to 3 × 180° = 540°

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

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

The Interior Angles of a Pentagon add up to 540°

The General Rule

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


ShapeSidesSum ofInterior AnglesShapeEach Angle
If it 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°
...........

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

So the general rule is:


Sum of Interior Angles = (n−2) × 180°

Each Angle (of a Regular Polygon) = (n−2) × 180° / n


Perhaps an example will help:


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

*


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

And for a Regular Decagon:

Each interior angle = 1440°/10 = 144°


Note: Interior Angles are sometimes called "Internal Angles"


Interior Angles Exterior Angles Degrees (Angle) 2D Shapes Triangles Quadrilaterals Geometry Index