Video Transcript
The internal angles of a
quadrilateral are in the ratio three to four to five to six. What is the largest angle?
We’ve been given some information
about the breakdown of four angles in our quadrilateral. So let’s recall what we actually
know about the interior or internal angles of a quadrilateral. We know that they sum to 360
degrees. So what we’re going to need to do
is share 360 degrees into a given ratio. And there are two ways we can do
this. We’ll consider both methods. Let’s consider the first
method.
In our first method, we begin by
adding the ratios together. That’s three plus four plus five
plus six, which is equal to 18. Our second step is to divide our
amount, whatever that is, by this number. Here, that’s to divide 360 by
18. In doing so, we’re finding the size
of one part in our ratio. 36 divided by 18 is two, so 360
divided by 18 is 20. And this means that one part in our
ratio is worth 20 degrees.
The third and final step is to
multiply each part of our ratio by this number. But we’re not going to perform that
fully. We’re just looking to find the size
of the largest angle. In our ratio, that’s represented by
the six. Since we know that one part is
worth 20 degrees, we’re going to multiply six by 20. Six times 20 is 120. And so the largest angle in the
quadrilateral is 120 degrees. Now, what we could do is multiply
the other three parts and check these add to make 360. It’s a good way to check our
answer.
But let’s consider the other
method. The first step in this other method
is the same. We add the ratios. The next step is to form a fraction
for the parts we are interested in. That might be all the parts, but
actually we’re just interested in the largest angle. So that’s the six. Since there are a total of 18
parts, and we’re interested in six of them, the fraction we’re interested in is six
eighteenths. The final step here is to find this
fraction of the amount.
Well, we know we’re sharing 360
degrees, so we’re going to find six eighteenths of 360. But six eighteenths simplifies to
one-third. So we’re going to find one-third of
360. And to find a third, we divide
through by three to get 120. And so, given the information about
the internal angles of our quadrilateral, we once again see that the largest angle
is 120 degrees.
