Video: Solving Problems Involving Adjacent Angles

Find the sum of the two adjacent angles from the given angles in the diagram.


Video Transcript

Find the sum of the two adjacent angles from the given angles in the diagram.

In the diagram, we can see a whole turn. And it’s been split into six different angles. But there are only three of those six angles that we’re given. This angle here is labelled as 22 degrees. The size of this angle is 88 degrees. And the only other angle that we know is this one here, and it’s 64 degrees. The first keyword that we come across in our problem is the word “sum,” find the sum, although sometimes you might hear people using the words sum to mean calculation ⁠— I’m going to work out my sums. Really, we shouldn’t use it like this. It means something very definite in maths. And it means to add together. So to find the sum of something is to find the total.

So what do we need to find a total of? We need to find the sum of the two adjacent angles. And we’re told that these are the two adjacent angles from the given angles in the diagram. As we’ve just seen, we only have three given angles. So two of them must be adjacent. And we need to add those two adjacent angles together. Let’s remind ourselves what makes two angles adjacent. Well, the word adjacent means next door, too. But we can recognise adjacent angles because they have two things in common. Firstly, they share a common vertex. We know the vertex in an angle is the point from which the rays of the sides come from. When we have two angles that are adjacent, all the sides come from the same point.

Now, if we look at our diagram, we can see that the three labelled angles, in fact, all of the angles, do come from the same point. They all have a common vertex. So we can’t separate our three angles out that way. But as we’ve said already, there’s also something else that adjacent angles have in common. And this has got to do with the fact that they’re next door to each other. Adjacent angles also share a common side. In other words, one of the sides in the angles is shared between both angles. It’s part of them both. This is what makes them next door to each other or adjacent.

And if we remember this fact, we can spot which two angles are going to be adjacent out of the three that are labelled. It’s 64 and 88. They share a common vertex but also a common side. So to solve the problem, we need to find the sum of these adjacent angles. What is 64 plus 88? Four plus eight equals 12. Six tens plus eight tens equals 14 tens plus the 10 we’ve exchanged equals 15 tens. And because our answer is the total of two angles, we need to write it using a degrees symbol. Out of the given angles in the diagram, we know that the two adjacent angles are 64 degrees and 88 degrees. We know this because they share a common vertex and a common side. And so the sum of these two adjacent angles is 152 degrees.

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