Step by step
The question
Question: find x.
The two lines are parallel.
The co-interior angles are x and 75°.
1 Use the angle fact
The arrows show the two lines are parallel.
Parallel lines go the same way.
They never meet.
A third line crosses both of them.
It is called a transversal.
Our two angles are between the parallel lines, on the same side of the transversal.
They are called co-interior angles, or same-side interior angles.
Together they make a C shape.
Co-interior angles add up to 180°.
Why?
Look at this angle at the top.
It is in the same place as the bottom angle, so they are equal.
With our top angle, it makes a straight line: 180°.
Careful: they are not equal.
They add up to 180°.
So we add them and make it 180: x + 75 = 180.
2 Remove the + 75
We want x by itself.
The + 75 is in the way.
To remove + 75, we take away 75.
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.
+ 75 and − 75 make zero.
Cross them out.
180 − 75 = 105.
So x = 105!
3 Check
Let's check: put x = 105 back and add the angles.
They add up to 180°.
So x = 105 is right!
Let's look back.
First: use the angle fact.
Then: remove the + 75.
Last: check.