How_To_Be_Good_At_Math

246 GEOMETRY •^ ANGLES INSIDE POLYGONS

Angles inside polygons

More sides means bigger angles

All the angles in a regular polygon are the same size. So, if you know one

angle, you know them all. Look at these polygons. You can see that the

more sides a regular polygon has, the larger its angles become.

Angles inside regular and irregular polygons

The angles inside polygons with the same number of sides always add up

to the same amount. Let's look at the angles inside two different hexagons.

All angles

are 120°

Polygons get their names from the number of their sides

and angles. We learned about polygons' sides on pages

218-19. Now we're going to focus on their angles.

97º

152º 113º

120º

110º

128º

The sum of the angles

inside a polygon

depends on how many

sides it has.

Pentagon Hexagon Heptagon Octagon

108° 120° 128.6° 135°

8 sides and

8 angles

7 sides and

7 angles

6 sides and

6 angles

5 sides and

5 angles

Regular hexagon

The angles inside this regular hexagon are

all the same size. The six angles of 120° add

up to a total of 720°.

Irregular hexagon

In this irregular hexagon, each angle is

different. But when you add them up, the total is

720° – the same as for the regular hexagon.

246_247_Angles_inside_polygons.indd 246 29/02/2016 18:05