Step by step
The question
Question: if the exterior angle is 5x° and the far inside angles are 2x° and 75°, 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 2x + 75 = 5x.
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 2x from the left side.
To remove 2x, we take away 2x.
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.
2x and − 2x make zero.
Cross them out.
5x − 2x = 3x.
Now we have 75 = 3x.
Let's swap the two sides, so x is on the left.
3 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.
75 divided by 3 is 25.
So x = 25!
4 Check
Let's check: with x = 25, the inside angles are 50° and 75°.
Together 125°, 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 3.
Last: check.