Step by step
The question
Question: find what kind of triangle has angles x, 45°, 45°.
1 Find the missing angle
The three angles in a triangle add up to 180°.
So x + 45 + 45 = 180.
2 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
Plain numbers go together.
45 + 45 = 90.
Now we have x + 90 = 180.
3 Remove the + 90
We want x by itself.
The + 90 is in the way.
To remove + 90, we take away 90.
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.
+ 90 and − 90 make zero.
Cross them out.
180 − 90 = 90.
So x = 90!
4 Find the biggest angle
The biggest angle is 90°.
Only the biggest angle decides the name.
It is exactly 90°: a right angle.
Careful!
Every triangle has at least two acute angles.
So they do not decide.
Only the biggest angle does.
5 Name it
So the triangle is right.
6 Check
Let's check: the angles must add up to 180°.
They do.
So it is a real triangle, and it is right.
Let's look back.
First: find the missing angle.
Then: group like terms.
Then: remove the + 90.
Then: find the biggest angle.
Then: name it.
Last: check.