Step by step
The question
Question: find the base angles x of an isosceles triangle with top angle 52°.
1 Use the isosceles fact
Isosceles means two sides are equal.
The small marks show which two.
The third side, at the bottom, is the base.
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 x too.
2 Use the angle fact
The three angles in a triangle add up to 180°: x + x + 52 = 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.
x + x = 2x.
Now we have 2x + 52 = 180.
We want x by itself.
First we remove the + 52, so 2x is alone.
Then we remove the times 2.
Is x alone now?
Not yet: + 52 is still with x.
How do we remove it?
4 Remove the + 52
To remove + 52, we take away 52.
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.
+ 52 and − 52 cancel each other.
They make zero.
180 − 52 = 128.
Now we have 2x = 128.
So after step 4: we took away 52, and now we have 2x = 128.
Is x alone now?
Not yet: 2x means 2 times x.
5 Remove the 2
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
They cancel each other.
So just x is left.
128 divided by 2 is 64.
So x = 64!
6 Check
Let's check: put x = 64 back and add the three angles.
They add up to 180°.
So x = 64 is right!
Let's look back.
First: use the isosceles fact.
Then: use the angle fact.
Then: group like terms.
Then: remove the + 52.
Then: remove the 2.
Last: check.