Angles on a line 130 and x Easy

The question

Question: find x when the angles on a straight line are 130° and x.

1 Use the angle fact

Angles on a straight line add up to 180°.

A straight line is half a turn.

So we add them all and make it 180: 130 + x = 180.

2 Remove the 130

We want x by itself.

The 130 is in the way.

To remove 130, we take away 130.

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.

130 and − 130 make zero.

Cross them out.

180 minus 130 is 50.

So x = 50.

The angle x is 50°.

3 Check

Let's check: put x = 50 back and add the angles.

They add up to 180°.

So x = 50 is right!

Let's look back.

First: use the angle fact.

Then: remove the 130.

Last: check.

▶ Watch it solved

Angles on a line x + 20 and 2x + 10 Medium

The question

Question: find x when the angles on a straight line are x + 20 and 2x + 10.

1 Use the angle fact

Angles on a straight line add up to 180°.

A straight line is half a turn.

So we add them all and make it 180: x + 20 + 2x + 10 = 180.

2 Group like terms

The x terms go together.

The plain numbers go together.

Now we have 3x + 30 = 180.

3 Remove the + 30

We want 3x by itself.

The + 30 is in the way.

To remove + 30, we take away 30.

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.

+ 30 and − 30 make zero.

Cross them out.

180 minus 30 is 150.

4 Remove the 3

3x means 3 times x.

We want just x.

To remove times 3, we divide by 3.

We do it on both sides, so they stay equal.

3 divided by 3 is 1.

So just x is left.

150 divided by 3 is 50.

So x = 50.

5 Check

Let's check: put x = 50 in each angle.

Now add all the angles.

They add up to 180°.

So x = 50 is right!

Let's look back.

First: use the angle fact.

Then: group like terms.

Then: remove the + 30.

Then: remove the 3.

Last: check.

▶ Watch it solved

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

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.

▶ Watch it solved