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4.1 H) Angle Rules – Parallel Lines: Part 2

4.1 H) Angle Rules – Parallel Lines: Part 2

The content is this section will use the rules that were discussed in the previous section. Make sure that you have gone through all of the rules in the previous section before working through this section (click here to be taken back to the previous section).

In most of the following examples, you will be able to find an unknown angle in a few different ways/ by using a few different rules. It does not matter which way/ rule you use to find the angle.

In most of the following examples, you will be able to find an unknown angle in a few different ways/ by using a few different rules. It does not matter which way/ rule you use to find the angle.

**Example 1**

What is the size of angle

*a*and

*b*? Give reasons for your working.

Angle

Angle

*a*will be 100°. This is because vertically opposite angles are equal.Angle

*b*is also going to be 100° and this is because of the corresponding angle rule. The F for the corresponding angle rule is shown below.**Example 2**

What is angle

*c*and

*d*?

Let’s start by finding

*c*.*c*is going to be 60° because of the alternate angle rule. The alternate angle rule is also known as the Z rule and the Z is shown on the diagram below.There are two different ways that we are able to find

*d*. We can either use the rule that angle on a straight line add up to 180° (*c*+*d*= 180°), or we can use the interior angle rule, which states that the angles that are on one side of the intersecting transversal and between the parallel lines add up to 180° (60 +*d*= 180°). We are able to create the same equation from both of these rules. The equation that we can create is given below:We find the value of

*d*by moving the 60 from the left side of the equation to the right. We are able to move the 60 by doing the opposite; we take 60 from both sides of the equation.Therefore, angle

*c*is 60° and angle*d*is 120°.**Example 3**

What angles in the diagram below are the same as each other?

Let’s start with angle

Let’s now look at angle

Therefore, the angles that are the same are:

I have colour coded the diagram, so that all of the angles that are the same are the same colour;

*a*and find all of the angles that are the same as*a*. Angle*a*is the same as*d*because of vertically opposite angles. Angle*d*is the same as*e*because of alternate angles (Z angles). Also, angle*d*is the same as*h*because of corresponding angles (F angle). Therefore, the angles*a*,*d*,*e*and*h*are all the same.Let’s now look at angle

*b*and find all of the angles that are the same as*b*. Angle*c*will be the same as*b*because of vertically opposite angles being the same. Angle*f*will be the same as*c*due to alternate angles (Z angles). And finally,*g*will be the same as*f*because of vertically opposite angles.Therefore, the angles that are the same are:

*a*,*d*,*e*and*h*are all the same- b,
*c*,*f*and*g*are all the same

I have colour coded the diagram, so that all of the angles that are the same are the same colour;

*a*,*d*,*e*and*h*are all green, and b,*c*,*f*and*g*are all orange.**Final Note**

Like I said earlier, there are many different ways that you can prove why an angle is the size that it is. Therefore, it does not matter which rule you use to explain your answer providing that you have explained it well. Make sure that when you are explaining the rules you over explain to ensure that you get all of the marks rather than under explaining, which may result in marks being lost.

It would be a good idea to have the names of these rule written down on a revision card. This is because the intuition from the rule is fairly easy to remember, but the names of the rules are quite easy to forget.