Step by step
The question
Question: find what kind of triangle has angles 40°, 65°, x.
1 Find the missing angle
The three angles in a triangle add up to 180°.
So 40 + 65 + x = 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.
40 + 65 = 105.
Now we have 105 + x = 180.
3 Remove the 105
We want x by itself.
The 105 is in the way.
To remove 105, we take away 105.
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.
105 and − 105 make zero.
Cross them out.
180 − 105 = 75.
So x = 75!
4 Find the biggest angle
The biggest angle is 75°.
Only the biggest angle decides the name.
75 is less than 90.
So all three angles are under 90°.
Careful!
For an acute triangle, even the biggest angle is under 90°.
5 Name it
So the triangle is acute.
6 Check
Let's check: the angles must add up to 180°.
They do.
So it is a real triangle, and it is acute.
Let's look back.
First: find the missing angle.
Then: group like terms.
Then: remove the 105.
Then: find the biggest angle.
Then: name it.
Last: check.