Step by step
The question
Question: find x when the angles in a triangle are 3x, 4x and 5x.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Use the angle fact
The three angles in a triangle always add up to 180°.
So we add them all and make it 180: 3x + 4x + 5x = 180.
2 Group like terms
The x terms go together.
Now we have 12x = 180.
Is x alone now?
Not yet: 12x means 12 times x.
How do we remove it?
3 Remove the 12
12x means 12 times x.
To remove times 12, we divide by 12.
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.
12 divided by 12 is 1.
They cancel each other.
So just x is left.
180 divided by 12 is 15.
So x = 15.
4 Check
Let's check: put x = 15 in each angle.
Now add all the angles.
They add up to 180°.
So x = 15 is right!
5 Pick the choice
Our answer is x = 15.
That is choice B.
6 Why not the others
A is 12.
Wrong: 3 + 4 + 5 = 12 is how many x's, not x.
C is 30.
Wrong: 360 ÷ 12: a triangle has 180°, not 360°.
D is 60.
Wrong: that is 4x, not x.
Let's look back.
First: use the angle fact.
Then: group like terms.
Then: remove the 12.
Then: check.
Then: pick the choice.
Last: why not the others.