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# Interior Angles of Polygons

## Triangles

### 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°

(A Quadrilateral is any shape with 4 sides)

### 80° + 100° + 90° + 90° = 360°

A Square adds up to 360°

Let's tilt a line by 10° ... still adds 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°)