Step by step
The question
Question: find x.
C and D are on the same side of AB.
The angles at C and D are x + 50 and 40°.
1 Use the circle rule
The line AB cuts the circle into two parts, called segments.
C and D are in the same part.
Both angles stand on the same arc: the orange part, from A to B.
Look at the angle at the center on that arc.
The circle rule says it is double each of them.
Both angles are half of the same angle.
So they are equal.
So the two angles are equal: x + 50 = 40.
2 Remove the + 50
We want x by itself.
The + 50 is in the way.
To remove + 50, we take away 50.
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.
+ 50 and − 50 make zero.
Cross them out.
40 − 50 = −10.
So x = −10!
3 Check
Let's check: put x = −10 in each angle.
We get 40°, the same as the other angle.
So x = −10 is right!
Let's look back.
First: use the circle rule.
Then: remove the + 50.
Last: check.