Video: AQA GCSE Mathematics Foundation Tier Pack 4 • Paper 1 • Question 13

Work out the size of 𝑥. And our shape is not drawn accurately.


Video Transcript

Work out the size of 𝑥. And our shape is not drawn accurately.

As I just stated, the shape is not drawn accurately. So therefore, we can’t just measure the angles to work out what 𝑥 is. Okay, so what are we gonna do? Well, we need to use one of our angle facts. And that one is that we know that the angles in a triangle sum to 180. And we also know that our triangle has a right angle cause it’s shown here by the small square. And a right angle is 90 degrees. So therefore, we can say that 90 add two 𝑥 add three 𝑥 is gonna be equal to 180. And that’s because these are the angles within our triangle. And they must sum to 180.

So what we can do next is collect like terms to simplify. And our like terms are two 𝑥 and three 𝑥. Well, two add three is five. So we have five 𝑥. So we’ve got 90 plus five 𝑥 is equal to 180. Well, we’re trying to find 𝑥. So we want 𝑥 on its own on the left-hand side of the equation. So what we’re gonna do is subtract 90 from each side of the equation. And that’s because if we subtract 90 from the left, we’re just left with our five 𝑥. And as we know, if we do one thing to one side of the equation, we must do the same thing to the other side of the equation. So subtracting 90 from each side, we get five 𝑥 is equal to 90. So great! We now know what five 𝑥s are.

So what we’re gonna want is to know what a single 𝑥 is because we want to find out the size of 𝑥. So to do that, we’re gonna have to divide each side by five. And we divide each side by five because five 𝑥 means five multiplied by 𝑥. So therefore, we want to do the inverse operation. So rather than multiplying by five, we’re gonna divide by five. So therefore, this gives us that 𝑥 is equal to 18. And it’s gonna be degrees.

And we could’ve worked that out in a couple of ways. One way would be to use the bus stop method or short division. So we see how many fives go into 90. So first of all, how many fives go into nine? Well, that’s once, with a remainder of four. So then, we see how many fives go into 40 because we carried the four. And eight fives are 40. So therefore, we’ve got our answer of 18. So what we get is that the size of 𝑥 is equal to 18.

Okay, so what we’re gonna do is quickly check if this is the correct answer. And we can do that by working out each of the angles. So our first angle up here is two 𝑥. So it’s two multiplied by 18, which gives us 36. And then, our bottom angle is going to be three multiplied by 𝑥, which will be three multiplied by 18, which is 54 degrees. And we could do that mentally because three multiplied by 10 is 30. Three multiplied by eight is 24. 30 add 24 is 54.

And then, we can add these together to check to make sure they add up to 180. So in the units column, we’ve got six and four, which gives us 10. So we put a zero in the units column and carry the one till we got nine add three, which gives us 12. 12 add five is 17 add the one we carried is 18. So therefore, we get 180 degrees. And that’s correct because the angles in a triangle do sum to 180 degrees.

So we can say that, definitely, the size of 𝑥 is 18 degrees.

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