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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:


