How_To_Be_Good_At_Math

quadrilaterals Calculating angles inside

Find the missing angle

So, now we know that the angles in a quadrilateral add up to 360°.

We can use this fact to work out missing angles in quadrilaterals.

130º

95º

75°

Now let's take 300°

away from 360°:

360° − 300° = 60°

So the missing

angle is 60º.

Look at this shape. What's

the missing angle?

We know that three of the

angles are 75°, 95°, and

130°. Lets add them together:

75° + 95° + 130° = 300°

Put the angles round a point

You can tear the corners off a

quadrilateral and arrange them

round a point, like this. We know

that angles round a point add up

to 360°, so the quadrilateral's

angles must add up to 360°, too.

Make triangles

A quadrilateral can be split into

two triangles, like this. We know

that the angles in a triangle add up

to 180º. That means the angles in a

quadrilateral add up to 2 × 180º,

which is 360º.

Draw a dividing

line between

opposite vertices

Rearrange the

corners to fit

round a point

Tear off the

four corners

?

Calculating angles

inside quadrilaterals

The angles inside a quadrilateral always add up to 360°.

There are two ways we can prove that this is true.

The angles inside a

quadrilateral always

add up to 360°.

244_245_Angles_in_quads.indd 245 29/02/2016 18:05