What you need to know
Parallel lines: 4 Simple rules
Parallelmeans that two lines are always the same distance away from each other, and therefore will never meet never meet. Parallel lines are marked with matching arrows.
Drawing a straight line that passes right through two parallel lines creates a whole bunch of angles which are related to all the other angles. How these angles are related is explain in these 4 simple rules.
Alternate Angles:
Alternate angles are the same.
D = C
They are found in aZ-shape, and sometimes called “Zangles“
Corresponding Angles
Corresponding angles are the same.
F = E
They are found in an F-shape and are sometimes called “Fangles“
Vertically aligned angles
Vertically aligned angles are the same
A + B
These are angles around a point, always opposite from one another.
Interior / Aligned angles
Allied angles add up to 180\degree
H + G = 180\degree
These can be refereed to as either Allied angles or Interior angles
These form a C-Shape.
Example:
Find the angle marked x in the picture below.
BD and EG are parallel lines.
State which angle fact you used at each step.
Currently we cannot see a rule connecting \angle EFC with x
This means we will need multiple steps. (there are a few ways to do this)
Firstly, we will use the fact that angles on a straight line add to 180.
Specifically, angle \angle EFC and angle \angle GFC add to make 180\degree.
Which means we can do the following:
\angle CFG = 180\degree - 32\degree = 148\degree.
Now, looking at the diagram we can see that angle \angle CFG and the missing angle x are corresponding angles.
Therefore, we get
x = 148\degree.
As mentioned, there are multiple ways to do this question. How else might you do it?
Example Questions
1) BD and EG are parallel lines. Find the angle marked x in the picture below. State which angle fact you use at each step.
Firstly, because angle HFG and angle EFC are vertically opposite, we get
\text{angle EFC } = 48\degree
Secondly, because angle EFC and angle BCA (angle x) are corresponding angles, we get
\text{angle BCA } = x = 48\degree
There are other possible methods for doing this question. As long as you’ve correctly applied angle facts, explained each step, and got the answer to be 48\degree, your answer is correct.
2) CE and FH are parallel lines. Find the angle marked x in the picture below. State which angle fact you use at each step.
Firstly, using the fact that angles FGJ and CDG are corresponding angles, we get
\text{angle CDG } = 121\degree.
Secondly, because angles on a straight line add to 180, and angles CDG and CDA are on a straight line, we get
\text{angle CDA } = 180 - 121 = 59\degree.
Thirdly, again using the fact that angles on a straight line add to 180, and angles CDA, BDE, and ADB (otherwise known as angle x) are on a straight line, we get
x + 50 + 59 = 180,\text{ so } x = 180 - 109 = 71\degree.
3) CF and GJ are parallel lines. Find the angle marked x in the picture below. State which angle fact you use at each step.
Firstly, because angles BEF and EHJ are corresponding angles, we get
\text{angle EHJ } = 39\degree.
Next, because angles EDH and DHG are alternate angles, we get
\text{angle DHG } = 76\degree.
Then, because angles DHG, DHE, and EHJ are angles on a straight line and angles on a straight line add to 180, we get
\text{angle DHE } = 180 - 76 - 39 = 65\degree
Finally, because angle DHE and angle x are vertically opposite angles, we get
x = 65\degree.
There are other possible methods for doing this question. As long as you’ve correctly applied angle fact, explained each step, and got the answer to be 71\degree, your answer is correct.
Worksheets and Exam Questions
MME Geometry Problems
Level 3-5Angles
Level 1-3Angles 2
Level 4-5Estimating and Measuring Angles
Level 1-3Angles Parallel Lines
Level 4-5Angles of Polygons
Level 4-5Related Topics
Geometry Basics Foundation Worksheets, Questions and Revision
Level 1 Level 2 Level 32D Shapes and Quadrilaterals Worksheets, Questions and Revision
Level 1 Level 2 Level 3Interior and Exterior Angles Worksheets, Questions and Revision
Level 4 Level 5Learning resources you may be interested in
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