Step by step
The question
Question: if the exterior angle is (6x − 5)° and the far inside angles are 3x° and 55°, 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 3x + 55 = 6x − 5.
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 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.
6x − 3x = 3x.
Now we have 55 = 3x − 5.
Let's swap the two sides, so x is on the left.
We want x by itself.
Two things are stuck to x: times 3 and − 5.
The − 5 is on the outside, so it comes off first.
Then the times 3.
3 Remove the − 5
To remove − 5, we add 5.
We do it on both sides, so they stay equal.
− 5 and + 5 make zero.
Cross them out.
55 + 5 = 60.
Now we have 3x = 60.
4 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, so they stay equal.
3 divided by 3 is 1.
So just x is left.
60 divided by 3 is 20.
So x = 20!
5 Check
Let's check: with x = 20, the inside angles are 60° and 55°.
Together 115°, 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 − 5.
Then: remove the 3.
Last: check.