 #### Revision Notes

##### What is a polygon?

A polygon is a flat (plane) shape with n straight sides.

eg A triangle is a polygon with 3 sides

eg A quadrilateral polygon with 4 sides

eg A pentagon is a polygon with 5 sides

In a regular polygon all the sides are the same length and all the angles are the same

eg A regular polygon with 3 sides is an equilateral triangle

eg A regular polygon with 4 sides is a square

##### Working with angles in polygons
1. TOTAL OF INTERIOR ANGLES = 180° × (n – 2)
(because the polygon can be split into n -2 triangles)
2. TOTAL OF EXTERIOR ANGLES = 360°
(this exterior angles rule is the same for ANY number of sides!)

eg For a hexagon (n=6):

a + b + c + d + e + f = 180° × (6 – 2) = 720°

p + q + r + s + t + u = 360°

For REGULAR Polygons:

For REGULAR Polygons:

3. EXTERIOR ANGLE = 360 ÷ n

4. INTERIOR ANGLE = 180 – Exterior Angle

#### Example

The diagram shows an irregular pentagon.
Work out the value of x.

This is an irregular pentagon (5 sides) so:

1. Total Interior Angles=180(5-2)=540°

Putting in the information from the diagram gives:

(3x + 5) + x + (x + 40) + 95 + (2x – 20)  =  540

Simplifying:

7x + 120  =  540

And solving:

7=  420

=  60

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