Step by step
The question
Question: find x.
The angle at the center is 100°.
The angle at the edge is x + 15.
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 the angle at the edge is half of the angle at the center: x + 15 = 100/2.
100 divided by 2 is 50.
2 Remove the + 15
We want x by itself.
The + 15 is in the way.
To remove + 15, we take away 15.
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.
+ 15 and − 15 make zero.
Cross them out.
50 − 15 = 35.
So x = 35!
3 Check
Let's check: put x = 35 in each angle.
Now double the angle at the edge.
100° is double 50°.
So x = 35 is right!
Let's look back.
First: use the circle rule.
Then: remove the + 15.
Last: check.