Step by step
The question
Question: the bearing of B from A is 040°: find the bearing of A from B.
1 Draw the north line
A bearing starts at the north line.
It is measured clockwise, the way a clock turns, and written with 3 figures.
At B we draw a north line too.
The two north lines are parallel.
2 Turn round
From B back to A is the opposite direction: half a turn more, 180°.
40 plus 180 is 220°.
back bearing = 040° + 180° = 220°
Why 180?
The north lines are parallel.
The angles between the path and the two north lines add up to 180°, as in the parallel lines lesson.
the north lines are parallel:
co-interior angles add to 180°
Careful!
A bearing is never negative.
Under 180°, we add 180.
Careful: not 40 − 180 = −140° ✗
3 Check
Let's check: the two bearings differ by exactly 180°, half a turn.
So it is right!
040° and 220° differ by 180°
Let's look back.
First: draw the north line.
Then: turn round.
Last: check.
Answer
Careful: not 40 − 180 = −140° ✗