Step by step
The question
Question: find the other angles of a rhombus with one angle of 64°.
1 Use the rhombus facts
A rhombus has four equal sides.
Its opposite sides are parallel.
It is the same on both sides of the dashed line from top to bottom.
So the opposite angle is 64° too.
The same goes for the top and bottom angles: both are x.
The top side and the bottom side are parallel.
So the two angles next to each other, 64° and x, are co-interior angles.
They add up to 180°.
So 64 + x = 180.
Careful!
Only the opposite angles are equal.
Angles next to each other add up to 180°.
2 Remove the 64
We want x by itself.
The 64 is in the way.
To remove 64, we take away 64.
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.
64 and − 64 make zero.
Cross them out.
180 − 64 = 116.
So x = 116!
3 Check
Let's check: put x = 116 back and add all four angles.
A shape with 4 sides has angles that add up to 360°.
So x = 116 is right!
The angles are 64°, 116°, 64° and 116°.
Let's look back.
First: use the rhombus facts.
Then: remove the 64.
Last: check.