Written theory

We have learn so far that a right angle is 90 degrees and straight line, or a straight angle is 180 degrees. We are going to use this last property to help us calculate unknown angles.
Look at this picture:

 

 

 

 

 

Here you see that 2 straight lines intersect and form a cross. We see that S1 is 50 degrees. We also see that S1 and S2 make a straight line.

So this means that S1 + S2 = 180. Now we know how many degrees S1 is. So we can also figure out how big S2 is. Because S2 = 180 – 50, So S2 = 130 degrees (because S1 and S2 are a straight line).

Now if I look at S1 and S4 they also make a straight line. So I can also calculate how big S4 is.
Because S1 + S4 = 180. We still know S1 is 50 degrees.

So S4 = 180 – 50 and that means S4 = 130 degrees (because S1 and S4 are a straight line).

As you can see S4 and S2 are the same. Now if we also calculate S3 with what we know we come to the conclusion that S3 = 180 – 130 = 50 degrees.

So we know that S3 and S1 are the same size as well.
This is true for all cases were 2 lines intersect. Opposite angles are the same size.

Here is some prove you can also find in your book:


Now there are to very important things you need to remember.

  1. This only works if the lines intersecting are straight. If a line bends at the intersecting point the opposite angles are no longer the same size. 
  2. You always have to write down in brackets why you say the angle is a certain size. E.g. angle S3 is 50 degrees (opposite angles). Or angle S2 = 180 – 50 = 130 degrees (straight angle)

You are now going to try and calculate angles. Make sure to use there rules: