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- Hello! My name is Mr. Clasper and in today's lesson, we're going to be looking at missing angles around a point and on a line.

Let's recap some angle facts.

In a quarter turn, we have 90 degrees.

In a half turn, there are 180 degrees and in a full turn, we have 360 degrees.

This diagram shows two angles around a point.

Now, we should know that these two angles have a sum of 360 as they represent a full turn.

Therefore, a plus b must be equal to 360 degrees.

Looking at this example, we now have a 250 degree reflex angle plus b.

But we know that together, these must have a sum of 360.

We could find the value of b by subtracting 250.

So this means that b would have to be 110 degrees.

This is because 110 plus 250 would give us our 360 degrees.

Let's have a look at this example.

We now have a 152 degree obtuse angle and the reflex angle b.

We know that these should have a sum of 360.

So again, if we subtract 152 from both sides, this would leave us with b is equal to 208 degrees.

And again, we can check this, because 208 plus 152 would give us 360.

Here are some questions for you to try.

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

And here are your solutions.

So just remember that your angle fact is that angles around a point must have a sum of 360.

Therefore, we can take each of our known angles away from 360 to get our solutions.

Let's take a look at this example.

This time we have three angles.

However, they still have a sum of 360 degrees as they are around the same point.

So we could set up an equation that looks like this.

We also know that 152 degrees plus 34 degrees would give us 186 degrees.

Therefore, 186 degrees plus c would have to be equal to 360 degrees.

From here, if we subtract 186, that leaves us with the solution of c being equal to 174 degrees.

Here are some questions for you to try.

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

And here are your answers.

So if we look at the example in the top right, finding angle m, one of our other angles does not have a label.

This is because it's indicated with a square, meaning that this is 90 degrees.

So we calculate with 90 degrees as well as the other two known angles.

For the bottom left example, we know that we have two angles which are both labelled c.

So if we subtract 230 from 360, we would get 130.

And this is the size of both of our angles c together.

So halving this will give us the value of c which would be 65.

Let's take a look at this example.

This time, we have angles on a straight line, or we can consider this the same as a half turn that we looked at at the start of the lesson.

A half turn has 180 degrees.

Therefore, a plus b must always be equal to 180 degrees.

Now, if we look at this example, we've been told that our acute angle is 34 degrees and if I add a, we know that this should be equal to 180 degrees.

Therefore, if I subtract 34 degrees from both sides of this equation, that leads us to the conclusion that a must be equal to 146 degrees.

Here are some questions for you to try.

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

And here are your solutions.

So again, just remember that the angle fact are the angles on a straight line must have a sum of 180 degrees.

Therefore, in each example you can subtract your unknown angles from 180 to find your missing angle.

Be careful with the last example.

So the angle on the left with the square, again, this means this is 90 degrees.

So you can calculate with 90 degrees and 56 degrees which should give you the answer y is equal to 34 degrees.

Here is another question for you to try.

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

And here is the solution.

So the angle 51 degrees and x must have a sum of 180 as they join at the same point and they're on a straight line.

The other 36 degree angle does not impact our answer at all as this is on a different point on the same straight line.

Let's take a look at this diagram.

We have two straight lines intersecting each other and we have the angles a, b, c, and d.

If we take a look at the highlighted blue line, we can see that a and b would have to have a sum of 180 degrees as they are on a straight line.

If we look at the other line highlighted in green, this means that c plus b must also be equal to 180.

Now, as a plus b and c plus b both equal 180, this must mean that a and c are equal.

This also means that b and d are equal.

What we learned from this fact is when we have two intersecting lines, vertically opposite angles are always equal.

Looking at this example, as our 52 degree angle is opposite our angle a, these two angles must be equal in size.

Therefore, a must be equal to 52 degrees.

Let's take a look at this example.

So the value of a is 124 degrees.

This is because a is vertically opposite the given angle, which is 124 degrees.

Now that I know this, I can add all four of my angles together, and I know that the angle sum must be 360 degrees.

And if I simplify further, that means that 248 degrees plus b plus c is equal to 360 degrees.

Subtracting 248 degrees from both sides of my equation would give me b plus c must be equal to 112.

Now, the last step, because b and c are both equal as they are opposite, that means I can halve 112 degrees, which gives me my angle size for b and c.

So half of 112 degrees or dividing 112 degrees by two would give me 56.

Therefore, b must be equal to 56 degrees and c must also be equal to 56 degrees.

Here are some questions you to try.

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

And here are your solutions.

So if we look at the first example, we know that a is equal to 70 degrees as it is vertically opposite the known angle.

And for the second part to question five, v must be equal to 110 degrees as it is vertically opposite the known 110 degree angle.

And from here, we can use our angles around a point as we know that they have a sum of 360 to find the value of u and t, knowing that u and t are also equal to each other.

And if we look at question six to ascertain whether a, b, c is indeed a straight line, we need to ensure that the angle sum is 180.

And if we add our three angles together, we do find that the add to 180.

Therefore, a, b, c must be a straight line.

And that brings us to the end of our lesson.

So I hope you've enjoyed learning about angles around a point and angles on a line.

Take care, I'll hopefully see you soon.