Step by step
The question
Question: if the exterior angle is (4x − 10)° and the far inside angles are (x + 20)° and 2x°, 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 + 20 + 2x = 4x − 10.
Careful!
The outside angle is not inside the triangle.
It does not go in the 180° sum.
2 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the x terms go together.
x + 2x = 3x.
Now we have 3x + 20 = 4x − 10.
3 Get x on one side
There is x on both sides.
We want x on one side only.
So we remove the 3x from the left side.
To remove 3x, we take away 3x.
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.
3x and − 3x make zero.
Cross them out.
4x − 3x = x.
Now we have 20 = x − 10.
Let's swap the two sides, so x is on the left.
4 Remove the − 10
We want x by itself.
The − 10 is in the way.
To remove − 10, we add 10.
We do it on both sides, so they stay equal.
− 10 and + 10 make zero.
Cross them out.
20 + 10 = 30.
So x = 30!
5 Check
Let's check: with x = 30, the inside angles are 50° and 60°.
Together 110°, the outside angle.
So the answer is right!
Let's look back.
First: use the rule.
Then: group like terms.
Then: get x on one side.
Then: remove the − 10.
Last: check.