Step by step
The question
Question: find x.
The angle at the center is 3x.
The angle at the edge is 42°.
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 is double 42: 3x = 2 × 42.
2 times 42 is 84.
2 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
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.
3 divided by 3 is 1.
So just x is left.
84 divided by 3 is 28.
So x = 28!
3 Check
Let's check: put x = 28 in each angle.
Now double the angle at the edge.
84° is double 42°.
So x = 28 is right!
Let's look back.
First: use the circle rule.
Then: remove the 3.
Last: check.