 So, two important theorems when dealing with triangles. The first is called the triangle sum theorem. Now every single triangle that we're going to deal with, if you take all of the interior angles, so for example, this angle, plus this angle, plus this angle, they'll always, always, always add up to 180 degrees. And this is a really important fact, and in fact I even have a short video demonstration to show you why it's true. Here's a quick demo to show you that the sum of the angles in any triangle is 180 degrees. So first off, I've got triangle ABC. I'm going to create a line that's parallel to AC through point B. And that line, you see it's parallel to AC. So it's parallel to AC. And now if we consider some of the other sides as transversals to these two parallel lines, kind of thinking back to previous chapters, this blue angle has an alternate interior angle pair. So these two blue angles are congruent because they're alternate interior angles. Now instead of that line, what if we consider this line? Well, that line is a transversal, crossing two parallel lines means that this red angle, angle A, is congruent to this angle because they're alternate interiors as well. So what that tells me is that, well, the red, the green, and the blue together form a straight line. In other words, they're almost like a linear triplet. And so those angles add up to 180 degrees. And it doesn't matter what the angle, what the triangle looks like, the original triangle. It can be obtuse, it can be right, scalene isosceles. It will always be the case that those three angles, the red, the green, and the blue, add up to 180 degrees. So then a related theorem is called the exterior angle theorem. It says each exterior angle of a triangle equals the sum of the two remote interior angles. There's a little bit of definitions that we'll need to deal with, an exterior angle. So an exterior angle occurs when you extend one of the sides of the triangle, we'll just take this triangle and extend one of the sides, if we extend it out we're talking about an exterior angle right there. So we're saying that exterior angle is equal to the sum of the two remote interior angles. So there are two of them, they're remote, remote as in far away or extreme. So the remote interior angles refer to these two angles, here's one of them and here's the other one. So what this theorem says, let's say if these angles were called angle one and angle two and this is angle three, the measure of angle three is equal to the sum of angle one and angle two. So we can use both of these theorems to solve a couple of problems coming up next.