Step by step
The question
Question: find the two equal angles x of a kite.
Its other angles are 130° and 72°.
1 Use the kite fact
A kite has two pairs of equal sides, side by side.
The marks show them.
Fold it on the dashed line from top to bottom.
The two halves fit exactly.
So the angles at the left and right corners are equal.
Both are x.
2 Use the angle fact
The other dashed line cuts the kite into 2 triangles.
2 times 180° is 360°.
So the 4 angles add up to 360°.
So x + x + 130 + 72 = 360.
Careful!
There are two equal 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.
Plain numbers go together.
x + x = 2x.
130 + 72 = 202.
Now we have 2x + 202 = 360.
We want x by itself.
Two things are stuck to x: times 2 and + 202.
The + 202 is on the outside, so it comes off first.
Then the times 2.
4 Remove the + 202
To remove + 202, we take away 202.
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.
+ 202 and − 202 make zero.
Cross them out.
360 − 202 = 158.
Now we have 2x = 158.
5 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just x is left.
158 divided by 2 is 79.
So x = 79!
6 Check
Let's check: put x = 79 back and add the four angles.
They add up to 360°.
So x = 79 is right!
Let's look back.
First: use the kite fact.
Then: use the angle fact.
Then: group like terms.
Then: remove the + 202.
Then: remove the 2.
Last: check.