Step by step
The question
Question: find the other angles of a rhombus with one angle of 115°.
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 115° 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, 115° and x, are co-interior angles.
They add up to 180°.
So 115 + x = 180.
Careful!
Only the opposite angles are equal.
Angles next to each other add up to 180°.
2 Remove the 115
We want x by itself.
The 115 is in the way.
To remove 115, we take away 115.
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.
115 and − 115 make zero.
Cross them out.
180 − 115 = 65.
So x = 65!
3 Check
Let's check: put x = 65 back and add all four angles.
A shape with 4 sides has angles that add up to 360°.
So x = 65 is right!
The angles are 115°, 65°, 115° and 65°.
Let's look back.
First: use the rhombus facts.
Then: remove the 115.
Last: check.