Angles Rules

Someone has emailed asking for help with Angle Rules.

There are many questions that involve working out angles that could come up on your exam. They will usually involve two things:
- Having to work out the size of an angle
- Having to give a reason for your answer

Giving a reason for your answer simply means justifying how you worked out the size of the angle. The text in italics throughout this post are examples of the reasons you should give for the corresponding questions.

Angles on a straight line add up to 180∘

Therefore, the angle marked a will be
180 - 45 = 135∘ (angles on a straight line add up to 180∘)

Where two straight lines cross, angles such as x and 40∘in the picture are called vertically opposite angles, and are equal.

x = 40∘(vertically opposite angles)


Angles - Parallel Lines

When we have two parallel lines (marked by arrows in the picture and on your exam), and another line that crosses both parallel lines, we have a few rules about the angles that are formed.

Angle p and the angle of 40∘are called corresponding angles, and are equal.

p = 40∘(corresponding angles) 

Angle q and the angle of 40∘are called alternate angles, and are equal.

q = 40∘(alternate angles)

Angle r and the angle of 40∘are called interior angles (they are both next to each other, inside the 'c' shape formed by the lines), and together they add up to 180∘.

r = 180 - 40 = 140∘(interior angles)


Remember: The properties for corresponding, alternate, and interior angles are only true if you have parallel lines.

Top Tip: Use practice papers to see what types of questions come up on this topic.
Sometimes you may be given a diagram with angles and lines, and a statement like "Brian thinks these two lines are parallel. Show that he is wrong."
When faced with this type of question, check these properties to see if they hold true, and therefore to show whether or not the lines are parallel.

What's Next?
There is lots more angle work you could revise, such as circle theorems, angles in regular polygons (regular shapes like pentagons, hexagons, etc.) Look out for posts on these in the future!


As always, send your maths questions to mathshints@gmail.com, and follow updates on Twitter.

MH