Lesson video

Hello.

My name is Mr Clasper and today we're going to be finding angles inside special quadrilaterals.

Before we begin this lesson, if you haven't done so already, I would strongly recommend looking at a lesson on alternate corresponding and co interior angles.

As this will help you understand the content of today's lesson.

We're going to look at trapezium first.

Now trapezium has one pair of parallel sides.

This is important as it helps us ascertain other facts about trapeziums. Let's take a look at our trapezium.

If we highlight our parallel sides and our first transversal.

We should know from this that a plus b must have a sum of 180 degrees.

This is because these two angles are co-interior.

If I take my parallel lines again and look at my other transversal.

This means that c and d must also have a sum of 180 degrees.

Again, this is because these two angles are co-interior.

Let's have a look at this example.

Calculate the size of angle a.

Well in the trapezium, if I highlight my parallel sides and I highlight the transversal with the angle a on it.

We can see that the angle a and the angle which is 110 degrees are co-interior.

This means that these two angles have a sum of 180 degrees.

Therefore the size of angle a must be 70 degrees.

Here's some questions for you to try.

Pause the video to complete your task and click resume once you have finished.

And here are the solutions.

Remember a little tip is to highlight your parallel sides.

And then it makes it easy for you to identify any co-interior angles that you have.

Remember co interior angles have a sum of 180 degrees.

And this should help you with some of your problems. If we have a look at the bottom right example.

Just be careful with this one.

If we highlight the parallel sides which will be the base and the top of this trapezium.

We can see that m and 72 are actually alternate angles.

Which means that they are equal and that can help you into your problem.

The next examples we're going to be looking at parallelograms. Parallelograms have two pairs of parallel sides and they also have important angle properties.

If I take these two sides and duplicate them and place them to the top right of my parallelogram, I can see that I have to vertically opposite angles.

I have the angle a in the top right and I also have the top right interior angle of my parallelogram which must also be equal to a as these two angles are vertically opposite.

If I do this again with the other side until these two sides duplicate and place them to the top left of our shape.

Again, because I know that vertically opposite angles are equal that means our missing interior angle must be b.

Looking at our parallelogram we can see that opposite angles inside our parallelogram are equal and this will always be the case.

Here is some questions for you to try.

Pause the video to complete your task and click resume once you have finished.

And here are the solutions.

Remember when we're using parallelograms we know that the opposite angles in a parallelogram are always equal.

And also we can apply our co-interior rules.

If we find any co-interior angles they must have a sum of 180 degrees.

Our next examples involve kites.

One way to view with kites is as two isosceles triangles.

In our example if we look at the top isosceles triangle, we know that these two angles are going to be equal.

And if we look at the bottom isosceles triangle we know that these two angles are going to be equal.

Notice that on both sides, the total angle is a plus b.

And in our kite, that's what this would look like.

These two angles will always be equal in a kite.

Another way to think about this are the angles subtended by two unequal sides will always be equal in a kite.

Here's some questions for you to try.

Pause the video to complete your task and resume once you have finished.

And here are your solutions.

Remember with a kite there are two equal angles as well as two pairs of equal lengths.

And we can use this to help us find our solutions.

Here's your last question.

Pause the video to complete your task and click resume once you have finished.

And here is your solution.

If we have a look at this kite the angle BCD is actually 95 degrees.

This is because it lies on the straight line BCE.

Once we found this angle, we know that the angle opposite to BCA.

So the angle CDA is also 110 degrees.

As we have two equal angles inside a kite.

And once we have these three angles we can use what we know about angles inside a quadrilateral.

In that they must have a sum of 360 to find our final answer which is that w is equal to 45 degrees.

And that brings us to the end of our lesson.

Hope you feeling confident finding angles inside parallelograms and trapezium and Kites.

Why not show off this skill by trying our exit quiz.

I will hopefully see you soon.