Step by step
The question
Question: if the exterior angle is 140° and the far inside angles are 2x° and (3x + 15)°, 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 + 3x + 15 = 140.
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.
2x + 3x = 5x.
Now we have 5x + 15 = 140.
We want x by itself.
Two things are stuck to x: times 5 and + 15.
The + 15 is on the outside, so it comes off first.
Then the times 5.
3 Remove the + 15
To remove + 15, we take away 15.
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.
+ 15 and − 15 make zero.
Cross them out.
140 − 15 = 125.
Now we have 5x = 125.
4 Remove the 5
5x means 5 times x.
We want just x.
To remove times 5, we divide by 5.
We do it on both sides, so they stay equal.
5 divided by 5 is 1.
So just x is left.
125 divided by 5 is 25.
So x = 25!
5 Check
Let's check: with x = 25, the inside angles are 50° and 90°.
Together 140°, the outside angle.
So the answer is right!
Let's look back.
First: use the rule.
Then: group like terms.
Then: remove the + 15.
Then: remove the 5.
Last: check.