Step by step
The question
Question: find x when the angles on a straight line are 128° and x.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Use the angle fact
Angles on a straight line add up to 180°.
So we add them all and make it 180: 128 + x = 180.
Is x alone now?
Not yet: + 128 is still with x.
How do we remove it?
2 Remove the 128
We want x by itself.
The 128 is in the way.
To remove 128, we take away 128.
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.
128 and − 128 cancel each other.
They make zero.
180 minus 128 is 52.
So x = 52.
The angle x is 52°.
3 Check
Let's check: put x = 52 back and add the angles.
They add up to 180°.
So x = 52 is right!
4 Pick the choice
Our answer is x = 52°.
That is choice A.
5 Why not the others
B is 128°.
Wrong: the two angles are not equal: they add up to 180°.
C is 232°.
Wrong: 360 − 128: a straight line is 180°, not 360°.
D is 308°.
Wrong: 128 + 180: added instead of taking away.
Let's look back.
First: use the angle fact.
Then: remove the 128.
Then: check.
Then: pick the choice.
Last: why not the others.