Step by step
The question
Question: find x when two lines cross and the opposite angles are 3x + 10 and 5x − 20.
1 Use the angle fact
Where two lines cross, the opposite angles are equal.
They are called vertical angles.
So the two angles are equal: 3x + 10 = 5x − 20.
Now we solve it.
2 Get x on one side
There is x on both sides.
We want x on one side only.
So we remove the 3x from the left side.
To remove 3x, we take away 3x.
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.
3x and − 3x make zero.
Cross them out.
5x − 3x = 2x.
Now we have 10 = 2x − 20.
Let's swap the two sides, so x is on the left.
We want x by itself.
Two things are stuck to x: times 2 and − 20.
The − 20 is on the outside, so it comes off first.
Then the times 2.
3 Remove the − 20
To remove − 20, we add 20.
We do it on both sides, so they stay equal.
− 20 and + 20 make zero.
Cross them out.
10 + 20 = 30.
Now we have 2x = 30.
4 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just x is left.
30 divided by 2 is 15.
So x = 15!
5 Check
Let's check: put x = 15 in each angle.
Both angles are 55°.
They are equal, so x = 15 is right!
Let's look back.
First: use the angle fact.
Then: get x on one side.
Then: remove the − 20.
Then: remove the 2.
Last: check.