Matematika Ria
Tambahkan ke favorit Tambahkan ke favorit
link Tautkan di sini
Beranda Matematika RiaBeranda








Hak cipta © 2009
MatematikaRia.com

Interior Angles of Polygons

An Interior Angle is an angle inside a shape.

Triangles

The Interior Angles of a Triangle add up to 180°

90° + 60° + 30° = 180°

80° + 70° + 30° = 180°

   
It works for this triangle!

Let's tilt a line by 10° ...

It still works, because one angle went up by 10°, but the other went down by 10°

Quadrilaterals (Squares, etc)

(A Quadrilateral is any shape with 4 sides)

90° + 90° + 90° + 90° = 360°

80° + 100° + 90° + 90° = 360°

A Square adds up to 360°

Let's tilt a line by 10° ... still adds up to 360°!

The Interior Angles of a Quadrilateral add up to 360°

Because there are Two Triangles in a Square

The internal angles in this triangle add up to 180°

(90°+45°+45°=180°)

... and for this square they add up to 360°

... because the square can be made from two triangles!

Pentagon

 

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

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

And if it is a regular pentagon (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 internal angles add up to 540°)

The General Rule

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

      If it is a Regular Polygon..
Shape Sides Sum of
Internal Angles
Shape Each Angle
Triangle 3 180° 60°
Quadrilateral 4 360° 90°
Pentagon 5 540° 108°
Hexagon 6 720° 120°
... ... .. ... ...
Any Polygon n (n-2) × 180° (n-2) × 180° / n

That last line can be a bit hard to understand, so let's have one example.

Example: What about a Decagon (10 sides) ?

Sum of Internal Angles = (n-2) × 180° = (10-2)×180° = 8×180° = 1440°


And, if it is a Regular Decagon, then each internal angle = 1440°/10 = 144°