Step by step
The question
Question: find x.
The angle at the center is 3x + 10.
The angle at the edge is x + 25.
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 3x + 10 is double x + 25: 3x + 10 = 2(x + 25).
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.
3x − 2x = x.
Now we have x + 10 = 50.
4 Remove the + 10
We want x by itself.
The + 10 is in the way.
To remove + 10, we take away 10.
We do it on both sides, so they stay equal.
+ 10 and − 10 make zero.
Cross them out.
50 − 10 = 40.
So x = 40!
5 Check
Let's check: put x = 40 in each angle.
Now double the angle at the edge.
130° is double 65°.
So x = 40 is right!
Let's look back.
First: use the circle rule.
Then: open the brackets.
Then: get x on one side.
Then: remove the + 10.
Last: check.