Angles around a point x, 2x, 3x

Step by step

The question

Question: find x when the angles around a point are x, 2x and 3x.

1 Use the angle fact

Angles around a point add up to 360°.

That is one full turn.

So we add them all and make it 360: x + 2x + 3x = 360.

2 Group like terms

The x terms go together.

Now we have 6x = 360.

3 Remove the 6

6x means 6 times x.

We want just x.

To remove times 6, we divide by 6.

We do it on both sides.

Why both sides?

The = sign means both sides are the same amount.

If we change only one side, they are not the same any more.

6 divided by 6 is 1.

So just x is left.

360 divided by 6 is 60.

So x = 60.

The angle x is 60°.

4 Check

Let's check: put x = 60 in each angle.

Now add all the angles.

They add up to 360°.

So x = 60 is right!

Let's look back.

First: use the angle fact.

Then: group like terms.

Then: remove the 6.

Last: check.