Step by step
The question
Question: the bearing of D from C is 155°: find the bearing of C from D.
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 D we draw a north line too.
The two north lines are parallel.
2 Turn round
From D back to C is the opposite direction: half a turn more, 180°.
155 plus 180 is 335°.
back bearing = 155° + 180° = 335°
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 155 − 180 = −25° ✗
3 Check
Let's check: the two bearings differ by exactly 180°, half a turn.
So it is right!
155° and 335° differ by 180°
Let's look back.
First: draw the north line.
Then: turn round.
Last: check.
Answer
Careful: not 155 − 180 = −25° ✗