Step by step
The question
Question: find x.
The angles of a quadrilateral are 120°, 60°, 75° and x.
1 Find the angle sum
Pick one corner.
Draw lines from it to the other corners.
They cut the quadrilateral into 2 triangles.
There are always 2 fewer triangles than sides: 4 − 2 = 2.
Each triangle has 180°.
2 times 180 is 360.
2 Use the angle fact
The angles of the quadrilateral add up to 360°.
So we add them all and make it 360: 120 + 60 + 75 + x = 360.
3 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.
120 + 60 + 75 = 255.
Now we have 255 + x = 360.
4 Remove the 255
We want x by itself.
The 255 is in the way.
To remove 255, we take away 255.
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.
255 and − 255 make zero.
Cross them out.
360 − 255 = 105.
So x = 105!
5 Check
Let's check: put x = 105 back and add the angles.
They add up to 360°.
So x = 105 is right!
Let's look back.
First: find the angle sum.
Then: use the angle fact.
Then: group like terms.
Then: remove the 255.
Last: check.