Video: Finding the Measure of an Exterior Angle of a Triangle given the Measure of the Other Two Angles

In the figure, use the information given to determine ๐‘šโˆ ๐ด๐ถ๐ท.

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Video Transcript

In the figure, use the information given to determine the measure of angle ๐ด๐ถ๐ท.

Now in these types of questions, the first thing I do is actually mark on any angles I actually know or I can calculate. And I would start with angle ๐ต๐ด๐ถ. And I can say that angle ๐ต๐ด๐ถ is gonna be equal to 180 minus 88 which is 92 degrees. But in these questions, what I always say you must remember to do is not just calculate the angle but also give your reasoning. And our reasoning for this is that it is 92 degrees as angles on a straight line are equal to 180 degrees.

Okay, so fantastic, weโ€™ve worked out the first thing that we can which is angle ๐ต๐ด๐ถ. Well, the next angle we can move on to is angle ๐ต๐ด๐ธ. And we can see that angle ๐ต๐ด๐ธ is gonna be equal to 180 minus 145 which is equal to 35 degrees. And again, weโ€™ve got to give our reasoning for this. And our reasoning is, in fact, the same as the first angle which was angle ๐ต๐ด๐ถ. And that is itโ€™s as the angles on a straight line are equal to 180 degrees. Okay, so great, weโ€™ve now found two angles that we can. Letโ€™s now move on to the measure of the angle that weโ€™re looking to find. And thatโ€™s the angle ๐ด๐ถ๐ท.

So Iโ€™m gonna mark this now on our diagram. So weโ€™ve got angle ๐ด๐ถ๐ท is the one that weโ€™re actually looking for. So itโ€™s now that we can actually use some notation on our diagram to help us work out what angle ๐ด๐ถ๐ท is actually gonna be equal to cause we got these two arrows here. And they tell us that actually these two lines are parallel. So now, if I draw a little sketch of parallel lines, we can see two angles here that are gonna be the same. And theyโ€™re gonna be the same because, in fact, theyโ€™re alternate angels. And we know that alternate angles on parallel lines are, in fact, equal to each other.

Okay, so now we can use this to help us find out what the angle ๐ด๐ถ๐ท is actually equal to. Well, we can now see that angle ๐ด๐ถ๐ท is gonna be equal to angle ๐ต๐ด๐ถ plus angle ๐ต๐ด๐ธ because these two angles together make up our alternate angle which is alternate to angle ๐ด๐ถ๐ท. So this is gonna be equal to 92 plus 35 which gives us an answer of 127 degrees. And again, we give our reason which weโ€™ve already mentioned. And the reasoning behind this calculation is because theyโ€™re alternate angles on parallel lines. So, therefore, we can say, using the information that weโ€™ve been given, we can say that the measure of angle ๐ด๐ถ๐ท is equal to 127 degrees.

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