Angles around a point 3x, 4x, 5x, 6x

Step by step

The question

Question: find x when the angles around a point are 3x, 4x, 5x and 6x.

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: 3x + 4x + 5x + 6x = 360.

2 Group like terms

The x terms go together.

Now we have 18x = 360.

3 Remove the 18

18x means 18 times x.

We want just x.

To remove times 18, we divide by 18.

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.

18 divided by 18 is 1.

So just x is left.

360 divided by 18 is 20.

So x = 20.

4 Check

Let's check: put x = 20 in each angle.

Now add all the angles.

They add up to 360°.

So x = 20 is right!

Let's look back.

First: use the angle fact.

Then: group like terms.

Then: remove the 18.

Last: check.