Step by step
The question
Question: find x.
The angle at the center is 2x + 10.
The angle at the edge is 50°.
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 2x + 10 is double 50: 2x + 10 = 2 × 50.
2 times 50 is 100.
We want x by itself.
Two things are stuck to x: times 2 and + 10.
The + 10 is on the outside, so it comes off first.
Then the times 2.
2 Remove the + 10
To remove + 10, we take away 10.
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.
+ 10 and − 10 make zero.
Cross them out.
100 − 10 = 90.
Now we have 2x = 90.
3 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.
90 divided by 2 is 45.
So x = 45!
4 Check
Let's check: put x = 45 in each angle.
Now double the angle at the edge.
100° is double 50°.
So x = 45 is right!
Let's look back.
First: use the circle rule.
Then: remove the + 10.
Then: remove the 2.
Last: check.