### Video Transcript

In the figure, use the information given to determine the measure of angle ๐ด๐ถ๐ท.

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 ๐ต๐ด๐ถ. And I can say that angle ๐ต๐ด๐ถ 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, weโve worked out the first thing that we can which is angle ๐ต๐ด๐ถ. Well, the next angle we can move on to is angle ๐ต๐ด๐ธ. And we can see that angle ๐ต๐ด๐ธ is gonna be equal to 180 minus 145 which is equal to 35 degrees. And again, weโve got to give our reasoning for this. And our reasoning is, in fact, the same as the first angle which was angle ๐ต๐ด๐ถ. And that is itโs as the angles on a straight line are equal to 180 degrees. Okay, so great, weโve now found two angles that we can. Letโs now move on to the measure of the angle that weโre looking to find. And thatโs the angle ๐ด๐ถ๐ท.

So Iโm gonna mark this now on our diagram. So weโve got angle ๐ด๐ถ๐ท is the one that weโre actually looking for. So itโs now that we can actually use some notation on our diagram to help us work out what angle ๐ด๐ถ๐ท 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 theyโre gonna be the same because, in fact, theyโre 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 ๐ด๐ถ๐ท is actually equal to. Well, we can now see that angle ๐ด๐ถ๐ท is gonna be equal to angle ๐ต๐ด๐ถ plus angle ๐ต๐ด๐ธ because these two angles together make up our alternate angle which is alternate to angle ๐ด๐ถ๐ท. 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 weโve already mentioned. And the reasoning behind this calculation is because theyโre alternate angles on parallel lines. So, therefore, we can say, using the information that weโve been given, we can say that the measure of angle ๐ด๐ถ๐ท is equal to 127 degrees.