Step by step
The question
Question: find x when the angles on a straight line are 40°, 65° 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: 40 + 65 + x = 180.
2 Group like terms
The plain numbers go together.
Now we have 105 + x = 180.
Is x alone now?
Not yet: + 105 is still with x.
How do we remove it?
3 Remove the 105
We want x by itself.
The 105 is in the way.
To remove 105, we take away 105.
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.
105 and − 105 cancel each other.
They make zero.
180 minus 105 is 75.
So x = 75.
The angle x is 75°.
4 Check
Let's check: put x = 75 back and add the angles.
They add up to 180°.
So x = 75 is right!
5 Pick the choice
Our answer is x = 75°.
That is choice A.
6 Why not the others
B is 105°.
Wrong: 40 + 65: that is the two angles together.
C is 115°.
Wrong: 180 − 65: forgot the 40°.
D is 255°.
Wrong: 360 − 105: a straight line is 180°, not 360°.
Let's look back.
First: use the angle fact.
Then: group like terms.
Then: remove the 105.
Then: check.
Then: pick the choice.
Last: why not the others.