Angles in a triangle x + 10, 2x, 3x - 10

Step by step

The question

Question: find x when the angles in a triangle are x + 10, 2x and 3x − 10.

1 Use the angle fact

The three angles in a triangle always add up to 180°.

So we add them all and make it 180: x + 10 + 2x + 3x − 10 = 180.

2 Group like terms

The x terms go together.

The plain numbers go together.

Now we have 6x = 180.

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.

180 divided by 6 is 30.

So x = 30.

4 Check

Let's check: put x = 30 in each angle.

Now add all the angles.

They add up to 180°.

So x = 30 is right!

Let's look back.

First: use the angle fact.

Then: group like terms.

Then: remove the 6.

Last: check.