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- Hello and welcome to this online lesson on angle reviews, angles in parallel lines.

So without forever ado, what I'd really like you to do is to make sure that you've got that quiet space that you're in, that you can really concentrate, you can really learn and make something of this lesson.

This is our last one.

So final push on, let's go for it.

So make sure there's app notifications are silenced, that you've got your pen and paper to hand and if you've got one, that you've got your laptop ready and you've got everything ready to go and you're not gonna be disturbed for the next 10 minutes or so.

So without further ado, let's take it away with Mr. Thomas's lesson.

So for your try this today what I'd really like you to do is to think about the intersection here that's formed by two lines crossing.

I want you to think about what facts you can write down about any four angles formed by two straight line crossings that you see there.

So, with that, I want you to spend five minutes now pausing the video and having a go at that task.

Off you go.

Excellent, let's go through this try this then.

So the ones that I thought of were the following.

I thought of vertically opposite angles are, what are they? They are equal, aren't they, very good.

Vertically opposite angles are equal.

So I can say that those two angles there are equal.

And I can say that those two angles there are equal.

I also thought of this, what am I indicating there? Angles on a straight line sum to 180 degrees, right? Very good if you got that.

And then finally, I'm gonna mark that point there, why am I marking a point? Well the reason why is because angles around a point sum to 360 degrees.

Very good if you managed to get that, reason being, see that other straight line there? Cause the angles there are two times 180 degrees, which gives you 360.

Awesome work for manager to get that.

Let's move on, for our connect today then, what I want us to consider is the alternate interior angles and then alternate exterior angles.

So do you see this? Remember this is the interior region that we talk talk about and this is the transversal that cuts across them, right? So we've got alternate interior.

As you can see marked there and alternate interior just here.

They're on opposite sides of that transversal and they're both in the interior region.

Same here, but it's just the exterior region this time.

So you've got exterior there and then the exterior angles just there.

So we can see that they are of course equal, they're equal to each other.

There we go, each other.

So alternate angles are equal.

Very, very, very, very, very, very important justification.

So with corresponding and allied angles, what happens is they lie on the same side of a transversal.

So you can see there, they can lie on the same side and they're in different regions.

We see this one's in the interior region and this one's in the exterior region, right? What about allied angles? Well, do they look equal? We can see the allied angles sum to 180 degrees.

What about corresponding angles? Well corresponding angles are equal.

So just be really, really aware of that, that the allied angles you can clearly see sum to 180 degrees and then corresponding angles are equal.

So with that, what I'd like you to do here is for your independent tasks, to find various angles there that are equal to each other for corresponding and allied in particular.

And then I'd like you to think of as many pairs of angles as you can find that are equal to each other.

And you can add to give you 180.

Okay, so pause video now, I'm gonna give you nine minutes to do that.

Off you go.

So let's go through our answers then.

So for the pairs of corresponding angles that I had, you could have G and C and they would be equal.

Of course.

You could also have F and B, you could also have H and D, they would be equal to each other.

And then you could also have A and E.

They'd also be equal to each other.

So there's quite a few different options you could have there.

Really good if you manage the spot some of them.

And then the allied angles, well we know that C plus F would some give 180, they are allied.

We could also see of course that we've got D plus E.

We've also got E plus G some 180 degrees.

You've also got which other ones, if you've got B and G, what else have you got? You've got H and E, A sorry, haven't you? H and A.

Very good if you managed to get that and then that is it from what I can tell.

So very, very good if you managed to get some of those or all of them indeed.

Very, very good.

So for your explore today, what I'd like you to do is to use your knowledge from this lesson to find and justify the size of unknown angles in that diagram below.

So pause the video now, I'm gonna give you 10 minutes to have a think about how to do that and you can have a go to the best of your ability.

If you're still struggling or wanna go through the answer, I'll be available on the next slide.

Excellent, let's go through the answer then.

So I can say that this is gonna be equal to 110 degrees.

'Cause I could say vertically opposite angles here.

I could also say that C is going to be 70 degrees 'cause of this straight line.

I could say that A is gonna be vertically opposite so it's gonna be 70.

I could say that this J over here would be due to allied angles.

I could say that that would be the case.

That would be 110 degrees.

I could also say it correspond with that one there as well.

There are loads of different justifications, as long as you're using the correct angle, the very one that you're focusing on, then it's totally valid to do a lot of them.

I could say this one of course is allied with D down there, so that's gonna be 70 degrees.

I could also say on a straight line here.

I could then go vertically opposite here with I.

That is perfectly acceptable.

And then a straight line if I wanted to here.

Very good if you've got justifications around what we've done in today's lesson with regards to allied and corresponding, et cetera.

So for example, K could be corresponding with D down there.

A could be corresponding with I.

You could also have, if you really wanted to branch out the previous lesson, not in the remit of this, but if you wanted to branch out, you could say J is alternate D, et cetera.

So there's so many justifications there which are really good if you've got that, well done.

What about this one? Well we can say this one here is gonna be vertically opposite, 32.

With the 32 there, we can say this is gonna be vertically opposite, give us 30 and then we add them together, which gives us 62, subtract from 180, which would give us, what would that give us? M is equal to 118, right? Very good if you managed to get that, really, really clever 'cause of the interior angles in a triangle we can then say this bit here would be 118 degrees 'cause it's vertically opposite.

We can then say, down here we've got a corresponding angle, which gives us 30 degrees for that bit there.

We can then say, what could we do from there? Well what we could do is we could say that this, N, corresponds with the 32 just there, couldn't we? Or we could say angles in a straight line.

Very, very good if you managed to get that.

And then this one here we can say of course that it is vertically opposite with the 30 just there.

Very, very good if you managed to get that all without my help.

So I just wanna say, that's the end of our lesson and I'm just really, really amazed if you managed to keep up with all that.

'Cause it can be a little bit tricky at times just realising, oh, is that an interior, is that exterior, is that alternate or is that all sorts of things that kind of come up and corresponding, et cetera.

So if you've managed to keep up and you think, yeah, I've got this.

Cool, thank you so much Mr. Thomas, I just want you to potentially ask your carer or parent at home if they can get permission in order for you to share your work.

It'd be really amazing to see so much work.

You can tag us @OakNational and may even be able to see some of your work.

Be amazing to see loads of your stuff that you've done.

So make sure you smash that exit quiz that you do such a good job and prove to everyone that you've done such a great job by getting five out of five in that exit quiz.

From now, it's goodbye for me and stay safe.

Bye bye.