### Video Transcript

What is the measure of angle ๐๐ถ๐ต?

First of all, we could take a look at angle ๐ด๐ถ๐. And this is gonna be equal to 32 degrees. And the reason itโs equal to 32 degrees because triangle ๐ด๐ถ๐ is actually an isosceles triangle. And we know that because we actually have these markers on the diagram that show us that these two lengths are equal. Okay, great. So we found one angle. Letโs get on and find some more to help us find the angle that weโre looking for, which is ๐๐ถ๐ต.

Well, the next angle weโre gonna take a look at is angle ๐ด๐๐ถ. And this is gonna be equal to 180 minus 32 minus 32, which is equal to 116 degrees. And this is because the angles in a triangle add up to 180 degrees. And itโs actually worth noting at this point that when youโre calculating missing angles in a problem like this, you must give the reasoning for each angle. So as youโve seen, weโve said one is because of a triangle being isosceles and the other one is angles in a triangle. So make sure you do that for each stage.

The next angle weโre taking a look at is angle ๐ต๐๐ถ. And this is gonna be equal to 180 minus 116, which is equal to 64 degrees. And we get this because the angles on a straight line add up to 180. And we can actually see that the angles there, 116 and 64, are both on a straight line. Okay, great. Letโs move on to the next angle.

So next, we actually move on to angle ๐ถ๐ต๐. And this is actually also equal to 64 degrees. And this is because triangle ๐ต๐ถ๐ is isosceles. And therefore, the two angles ๐ต๐๐ถ and ๐ถ๐ต๐ must be equal.

Okay, great. One more angle to find. And this is the one that the questionโs looking for. And this is angle ๐๐ถ๐ต. And this is gonna be equal to 180 minus 64 minus 64, which is therefore equal to 52 degrees. And this is because, again, angles in a triangle add up to 180 degrees. So therefore, we can say that the measure of angle ๐๐ถ๐ต is equal to 52 degrees. And thatโs the final answer.

Just a quick recap of what we did, is we actually worked in stages to find different angles that we needed to allow us to work out the final angle of ๐๐ถ๐ต. The key thing to remember is that at each of our stages, we actually gave a reason. In these kind of questions, you must give a reason for the angles that you found. An example of this is our final angle, where we said that angle ๐๐ถ๐ต was equal to 180 degrees minus 64 degrees minus 64 degrees which was equal to 52 degrees. And this was because the angles in a triangle all added to 180 degrees. So there you go, weโve actually given a reason for how we found our answer.