How_To_Be_Good_At_Math

GEOMETRY • ANGLES AT A POINT 235

We know that if we turn a line all the

way round to where it started, it

makes a full turn, which is 360°.

Imagine that the line stops on its way

to making a full turn, creating new

lines that meet at the same point. The

angles formed all add up to 360°.

This time, there are four lines meeting

at a point. But it doesn’t matter how

many lines there are – the angles will

always add up to 360°.

If the angles that meet at a point are

called a, b, and c, we can write this

rule as a formula:

a + b + c = 360°

Angles at a point

Another rule of geometry is that angles that meet at a point

always add up to 360°. This rule helps us work out missing

angles when they surround a point.

Finding the missing angle round a point

We know that the three

angles round this point

add up to 360°.

We also know that one angle

is 160° and the other is 130°.

Let’s add these angles together:

160° + 130° = 290°

a

c b

360º

50º

115º

75º

120º

145º 100º

115º

Now let’s subtract that total

from 360°: 360° − 290° = 70°

This means that the missing

angle is 70°.

Let’s use the rule we’ve just

learned to find the missing

angle at this point.

160º

130º

?

Angles round a point

always add up to 360°.

234_235_Angles_Straight_Line.indd 235 11/03/2016 16:24