Step by step
The question
Question: find x.
PT is a tangent to the circle with center O.
The angle at O is 50°.
The angle at P is x.
1 Use the tangent rule
PT touches the circle at T, and nowhere else.
It is called a tangent.
OT goes from the center to the touch point: a radius.
The radius meets the tangent at a right angle: 90°.
This is always true for a tangent.
2 Use the angle fact
O, T and P make a triangle.
Its three angles add up to 180°.
So 50 + x + 90 = 180.
Careful!
The right angle at T is one of the three angles.
It goes in the sum too.
3 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
Plain numbers go together.
50 + 90 = 140.
Now we have 140 + x = 180.
4 Remove the 140
We want x by itself.
The 140 is in the way.
To remove 140, we take away 140.
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.
140 and − 140 make zero.
Cross them out.
180 − 140 = 40.
So x = 40!
5 Check
Let's check: put x = 40 back and add the three angles.
They add up to 180°.
So x = 40 is right!
Let's look back.
First: use the tangent rule.
Then: use the angle fact.
Then: group like terms.
Then: remove the 140.
Last: check.