Step by step
The question
Question: find x.
The angles of a quadrilateral are x + 90, 3x + 90, 90° and 90°.
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: x + 90 + 3x + 90 + 90 + 90 = 360.
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.
Plain numbers go together.
x + 3x = 4x.
90 + 90 + 90 + 90 = 360.
Now we have 4x + 360 = 360.
We want x by itself.
Two things are stuck to x: times 4 and + 360.
The + 360 is on the outside, so it comes off first.
Then the times 4.
4 Remove the + 360
To remove + 360, we take away 360.
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.
+ 360 and − 360 make zero.
Cross them out.
360 − 360 = 0.
Now we have 4x = 0.
5 Remove the 4
4x means 4 times x.
We want just x.
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
So just x is left.
0 divided by 4 is 0.
So x = 0!
6 Check
Let's check: put x = 0 in each angle.
Now add all the angles.
They add up to 360°.
So x = 0 is right!
Let's look back.
First: find the angle sum.
Then: use the angle fact.
Then: group like terms.
Then: remove the + 360.
Then: remove the 4.
Last: check.