Step by step
The question
Question: find x.
An isosceles triangle has top angle 4x and base angle 3x.
1 Use the isosceles fact
Isosceles means two sides are equal.
The small marks show which two.
Fold it on the dashed line, from the top to the middle of the base.
The two halves fit exactly.
So the two angles at the base fit on each other.
The base angles are equal.
So the other base angle is 3x too.
2 Use the angle fact
The three angles in a triangle add up to 180°: 4x + 3x + 3x = 180.
Careful!
There are two base angles.
Both go in the sum.
3 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.
4x + 3x + 3x = 10x.
Now we have 10x = 180.
4 Remove the 10
10x means 10 times x.
We want just x.
To remove times 10, we divide by 10.
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.
10 divided by 10 is 1.
So just x is left.
180 divided by 10 is 18.
So x = 18!
5 Check
Let's check: put x = 18 back and add the three angles.
They add up to 180°.
So x = 18 is right!
Let's look back.
First: use the isosceles fact.
Then: use the angle fact.
Then: group like terms.
Then: remove the 10.
Last: check.