Lesson video

Hello, my name is Mr. Clasper.

And today we're going to be finding angles in parallel lines with two transversals.

Before we begin this lesson, let's have a recap on some key facts, which we'll need to use.

The first one, in this figure, we have a pair of corresponding angles.

So corresponding angles appear on the same side of a transversal and they are both either above the given parallel lines or below the given parallel lines and corresponding angles are always equal.

In the next example, we have a pair of alternate angles, alternate angles appear on either side of the transversal, and they are both inside the given parallel lines.

Alternate angles are also equal.

And our final example, if we have two angles, which reside inside a pair of parallel lines and are on the same side of a transversal, these angles are co-interior, and co-interior angles have a sum of 180 degrees.

Let's take a look at this example.

We have a pair of parallel lines and two transversals, and we're asked to find the value of A and the value of B.

Now to do this, we need to think about each problem separately.

So I'm going to concentrate on the transversal on the left first of all, as I'm not going to need the transversal on the right for the time being.

Now looking at this figure, I can see that my 60 degree angle and the angle A are co-interior.

Therefore A and 60 must have a sum of 180, and therefore the value of A must be 120 degrees.

Now I'm going to have a look at the second transversal.

Looking at the second transversal, the relationship between our 112 degree angle and B, is that they are alternate.

Alternate angles are always equal, and therefore the value of B must be 112.

Let's have a look at this example.

We're going to adopt a similar strategy.

I'm going to identify my parallel lines and I'm going to take it one transversal at a time.

So let's take this one first.

So angle A and the angle 60 are both alternate and we know that alternate angles must be equal.

Therefore, the value of A must be 60 degrees.

Looking at my second transversal, I can see that B and my 103 degree angle are both corresponding.

And as they're both corresponding, that means they're equal.

Therefore the value of B must be 103 degrees.

Here are some questions for you to try.

Pause the video to complete your task, and click Resume once you're finished.

And here are your solutions.

So remember if you highlight your parallel lines, this will help you identify different rules.

So if we do that, we know that our 73 degree angle and A are co-interior with the transversal on the left.

This means that these have a sum of 180 and therefore A must be equal to 107 degrees.

And if you look at the second transversal, our 98 degree angle and B must also have a sum of 180, therefore B must be 82.

And again, for the second one, highlighting your parallel lines.

This means that D and our 124 degrees are both co-interior angles and have a sum of 180, and C and our 113 degree angle are also co-interior.

Here are some more questions for you to try.

Remember, it's often useful to highlight your parallel lines first.

Pause the video to complete your task, and click Resume once you're finished.

And here is another set of solutions.

So again, highlight your parallel sides and make sure you're focusing on one transversal followed by the other.

Which angle properties will help you for this question? Pause the video to complete this task and click Resume once you're finished.

And here is the solution.

So in the diagram given, we need to find pairs of angles, which have a sum of 180 degrees.

Once we find these pairs, we know that these two angles must be co-interior.

And then once we know that they're co-interior, we should be able to correctly identify which lines must be parallel.

So we should find that AC is parallel to BD.

So our two parallel lines are AC and BD.

Here is your last question.

You may need to apply other angle fact you know, to access this question.

Pause the video to complete your task and click Resume once you're finished.

And here is the solution to your final problem.

So again, try to find as many angles as you can, based on angle fact you know.

so when you get the two base angles for your triangle, the final fact you need to use would be that angles inside a triangle would have a sum of 180, and then we should get our solution of X is equal to 60 degrees.

And that is the end of our lesson.

So you've managed to find angles in parallel lines with two trans reversals.

Give the exit quiz a go.

I will hopefully see you soon.