### Video Transcript

We’ve been given a diagram and
we’re asked to calculate the measure of angle 𝐴𝐵𝐶.

So that’s this angle here, when I
go from 𝐴 to 𝐵 and then to 𝐶. The angle is currently labelled as
𝑦. So we’re going to need our formula
for the sum of the interior angles at some stage, so I’ve written that down again
here. And let’s look at what we’ve
got. If we count the number of sides in
the diagram, we have five sides, so 𝑛 is equal to five. So our strategy here, we can work
out the total sum of the interior angles by using this formula. We know three of them, so we’ll be
able to subtract that. And then the remaining two angles
are both labelled as 𝑦, which means they’re the same. So whatever is left over, if we
halve it, that will give us the measure of angle 𝐴𝐵𝐶. So let’s go through the working for
this.

So the sum of the interior angles
is 180 times three. That’s five minus two because there
were five sides, which gives us 540 degrees for the total sum. So this means that all of these
angles added together, so 121 plus 110 plus 85 plus two lots of 𝑦 must be equal to
540. Now we could write that down as an
equation. And now we have this equation, we
just need to go through the steps to solve it in order to work out the value of
𝑦. So first of all, if I just combine
those 121, 110, and 85 together, so now I have the equation two 𝑦 plus 316 is equal
to 540.

The next step to solving this would
be to subtract 316 from both sides of the equation, so now I have two 𝑦 is equal to
224. And then to find 𝑦, I can halve
both sides of the equation. And that gives me a final answer of
𝑦 is equal to 112 degrees.