Step by step
The question
Question: if the exterior angle is (2x + 20)° and the far inside angles are x° and 60°, what is x?
The exterior angle is outside the triangle, on the pushed-out side.
1 Use the rule
The exterior angle is the two far inside angles added together.
So x + 60 = 2x + 20.
Careful!
The outside angle is not inside the triangle.
It does not go in the 180° sum.
2 Get x on one side
There is x on both sides.
We want x on one side only.
So we remove the x from the left side.
To remove x, we take away x.
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.
x and − x make zero.
Cross them out.
2x − x = x.
Now we have 60 = x + 20.
Let's swap the two sides, so x is on the left.
3 Remove the + 20
We want x by itself.
The + 20 is in the way.
To remove + 20, we take away 20.
We do it on both sides, so they stay equal.
+ 20 and − 20 make zero.
Cross them out.
60 − 20 = 40.
So x = 40!
4 Check
Let's check: with x = 40, the inside angles are 40° and 60°.
Together 100°, the outside angle.
So the answer is right!
Let's look back.
First: use the rule.
Then: get x on one side.
Then: remove the + 20.
Last: check.