Step by step
The question
Question: find x.
AB is a diameter.
The angles at A and B are 35° and x.
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: 35 + x + 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.
35 + 90 = 125.
Now we have 125 + x = 180.
4 Remove the 125
We want x by itself.
The 125 is in the way.
To remove 125, we take away 125.
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.
125 and − 125 make zero.
Cross them out.
180 − 125 = 55.
So x = 55!
5 Check
Let's check: put x = 55 back and add the angles.
They add up to 180°.
So x = 55 is right!
Let's look back.
First: use the circle rule.
Then: use the angle fact.
Then: group like terms.
Then: remove the 125.
Last: check.