Step by step
The question
Question: find x.
AB is a diameter.
The angles at A and B are 2x and 50°.
1 Use the circle rule
AB goes through the center O.
It is a diameter.
It cuts the circle in half: two semicircles.
At the center, A and B make a straight line: 180°.
The angle at C, on the edge, is half of it: 90°.
A right angle.
2 Use the angle fact
The three angles in a triangle always add up to 180°.
So we add them all and make it 180: 2x + 50 + 90 = 180.
3 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
Plain numbers go together.
50 + 90 = 140.
Now we have 2x + 140 = 180.
We want x by itself.
Two things are stuck to x: times 2 and + 140.
The + 140 is on the outside, so it comes off first.
Then the times 2.
4 Remove the + 140
To remove + 140, we take away 140.
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.
+ 140 and − 140 make zero.
Cross them out.
180 − 140 = 40.
Now we have 2x = 40.
5 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.
40 divided by 2 is 20.
So x = 20!
6 Check
Let's check: put x = 20 in each angle.
Now add all the angles.
They add up to 180°.
So x = 20 is right!
Let's look back.
First: use the circle rule.
Then: use the angle fact.
Then: group like terms.
Then: remove the + 140.
Then: remove the 2.
Last: check.