Angles In Parallel Lines
We use arrowheads to indicate that 2 lines are parallel:-
When a line crosses 2 parallel lines it creates pairs of equal angles
In the diagram below x and y are interior angles.
Interior angles add up to 180°
so x + y = 180°
Here’s a video that explains interior (or co-interior angles) very clearly:-
What are corresponding angles? That’s best explained by a couple of examples. In the following diagrams; a and b and c and d are corresponding angles. Note that the lines that join up corresponding angles make an ‘F’ shape:-
Here’s a video that explains corresponding angles clearly and in detail:-
This diagrams shows 2 pairs of alternate angles.
Alternate angles are equal. Notice how the lines make a ‘Z’ shape.
Here’s a video to explain alternate angles in parallel lines:-
Bearings are measured clockwise from the North:-
To get a fuller understanding of all bearings, consider the compass. Can you work out each direction shown here as a bearing?
NE = 045
E = 090
SE = 135
S = 180
SW = 225
W = 270
NW = 315
Here’s a video that explains bearings in some detail:-
Here’s another video that walks through some Bearings exam questions:-
Parellel Lines and Bearings
You can use the fact that North lines are always parallel and knowledge of angle facts to work out bearings.
This is best illustrated with an example. In the following diagram, work out the bearing of B from A.
There are 2 possible approaches to answering this question. Both start with drawing the North line from A so that we have 2 parallel lines pointing North.
The first method we can use is based on the fact that co-interior angles add up to 180°
Therefore we know the angle below marked in red must be 180° — 135° = 45°
But remember bearings are measured clockwise from the North. So the bearing of B from A = 360 — 45 = 315 see the diagram below:-
Here’s an alternate solution based on.….alternate angles. Again we start by drawing the North line from A:-
Then we find the alternate angles (it helps to extend the line below A and highlight the ‘Z’ shape we’re looking for):-
Finally, remembering that bearings are always measured clockwise from the North we just have to calculate the answer:-