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Hello, my name is Mr. Clasper and today we're going to be finding missing angles inside a quadrilateral.

In today's lesson, we're looking at missing angles inside a quadrilateral.

If we take our quadrilateral, we can arrange all of the angles so that they appear around a point.

So we have our purple angle followed by the blue angle, followed by the red angle, followed by the green angle, and they fit nicely around a point.

This works for any quadrilateral.

As we know that the angle somewhere around a point is 360 degrees, this also means that the angles inside a quadrilateral also have a sum of 360 degrees.

Let's have a look at this example.

Calculate the size of angle A.

We know that all four of these angles have a sum of 360 degrees, so we can set up an equation.

If I add my known angles together, I can simplify the equation.

And if I subtract 273 degrees from 360 degrees, this will leave me with A, therefore, A must be equal to 87 degrees.

Let's try this example.

Calculate the size of angle A.

This question is different as we've been given an exterior angle, and we only have two known angles inside our quadrilateral.

If we look at the 154 degree angle given on the exterior, that means that our interior angle must be 206 degrees as these are both around a point.

From here, we know that our three known angles inside the quadrilateral plus A must have an angle sum of 360 degrees.

And if I simplify this, that means that 261 degrees plus A is equal to 360 degrees.

Subtracting 261 from 360 would leave us with A is equal to 99 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, the angle factor we need is that the sum of all of the angles inside the quadrilateral must be 360 degrees.

If we take a look to the last example, just be careful with this one, we actually need to find the reflex angle D which is outside of our quadrilateral.

To do this, if we find them missing interior angle first, which is 221 degrees, we can then use this to find the angle D by subtracting that from 360 degrees.

This is because these two angles are around a point, and angles around a point also have a sum of 360 degrees.

Let's take a look at this example.

Calculate the size of angle A.

Before I do this, I need to find the other missing interior angle.

Our 137 degree angle resides on a straight line.

So that means, that our interior angle must be 43 degrees.

Now that we have this information, we can approach the question in a very similar manner to previous examples.

So we know that our four interior angles must have a sum of 360.

I can simplify this.

And if I subtract 192 degrees from 360 degrees, this must mean that A is equal to 168 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, for each of these problems, it's important that we find as many interior angles as we can first, but we can use what we know about the relationship between interior and exterior angles.

And angles on a straight line most out up to 180, and this can help us.

Here's a question for you to try.

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

And here is your solution.

So remember, it's important to take this in steps, find as many angles as you can.

So the angle KPN is 85 degrees as it is vertically opposite the angle QPR.

And we can also find the angle KLN which is 108 degrees as it lies on a straight line with the angle 72, which is MLN.

Once we've done this, we have three of our interior angles in our quadrilateral, so we can subtract these from 360 degrees to give us a final answer of 77 degrees for the size of angle LKP.

Here is your last question.

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

And here is your solution.

So, we know that the angles, A, B, C and D are shared into the ratio of 9 to 4 to 13 to 10.

But we also know that these four angles must have a sum of 360 degrees as they lie within a quadrilateral.

So if we share 360 degrees into the ratio of 9 to 4 to 13 to 10, we will get the angles 90 degrees, 40 degrees, 130 degrees, and 100.

Now, because D is 100 degrees, this means that E must be 80 degrees, and the ratio of D to E must therefore be 100 to 80.

And if we simplify this, we could get 10 to 8, and we can simplify that further to get our final answer of 5 to 4.

And that brings us to the end of our lesson.

I hope you've enjoyed finding missing angles in quadrilaterals and also solving problems. Just remember that those angles have a sum of 360 degrees.

Why not try our exit quiz just to boost your confidence and show how much you've learned.

I will hopefully see you soon.