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: (Note: it is a Regular Polygon when all sides are equal, all angles are equal.)

Interior Angle## Triangles

## The Interior Angles of a Triangle add up to 180°

## 90° + 60° + 30° = 180°

## 80° + 70° + 30° = 180°

It still works, because one angle went

upby 10°, but the other wentdownby 10°## Quadrilaterals (Squares, etc)

(A Quadrilateral is any shape with 4 sides)## 90° + 90° + 90° + 90° = 360°

## 80° + 100° + 90° + 90° = 360°

## The Interior Angles of a Quadrilateral add up to 360°

## Because there are Two Triangles in a Square

(90°+45°+45°=180°)

360°... because the square can be made from two triangles!

## Pentagon

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:(Note: it is a Regular Polygon when all sides are equal, all angles are equal.)

Regular Polygon...Internal Angles

°°°°°°°°(or Septagon)°°°°Any Polygonnn-2) × 180°n-2) × 180°/n## Example: What about a Regular Decagon (10 sides) ?

n-2) × 180°## (

10-2)×180° =8×180°1440°And it is a Regular Decagon so:

Each internal angle = 1440

°/10 =144°||