Step by step
The question
Question: find x.
The angle at the center is 4x.
The angle at the edge is x + 30.
1 Use the circle rule
O is the center of the circle.
Lines from A and B to the center make the angle at the center.
Lines from A and B to C, on the edge, make the angle at the edge.
Both angles stand on the same arc: the orange part of the circle, from A to B.
Circle rule: the angle at the center is double the angle at the edge.
This is always true.
So 4x is double x + 30: 4x = 2(x + 30).
2 Open the brackets
The 2 in front of the bracket multiplies every part inside.
So we write 2 times each part.
Work out each multiplication.
3 Get x on one side
There is x on both sides.
We want x on one side only.
So we remove the 2x from the right side.
To remove 2x, we take away 2x.
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.
2x and − 2x make zero.
Cross them out.
4x − 2x = 2x.
Now we have 2x = 60.
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.
60 divided by 2 is 30.
So x = 30!
5 Check
Let's check: put x = 30 in each angle.
Now double the angle at the edge.
120° is double 60°.
So x = 30 is right!
Let's look back.
First: use the circle rule.
Then: open the brackets.
Then: get x on one side.
Then: remove the 2.
Last: check.