Everyone, welcome back. So in a previous video, we learned complementary angles add up to 90 degrees, and supplementary angles add up to 180 degrees. But some problems, like the one we're going to work out down here, will throw at you some shapes or diagrams or even triangles that will have the angles that are written in terms of variables like x. They won't give you an angle and ask you for the complement or supplement. They'll give you something like this. Now it might seem like we have to use a different method to solve these types of problems, but we actually use what we know about complementary and supplementary angles to solve them. Let me just go ahead and show you using this example over here. We'll walk through it together, and I'll show you how this works. Alright?
So this is a right triangle over here. We have a right triangle with this little square in the corner. That means that that's 90 degrees. So how do we solve this problem here? Up until now, whenever we have triangles, we usually know what 2 of the angles are; we could solve for the other one, because we know all the angles in a triangle add up to 180 degrees. Well, the whole idea here is if this is fixed at 90 degrees in a right triangle, because one angle is fixed at 90, the other two angles over here, these two have to also be 90. So those two angles are also going to be complementary. So how can we use this to help us solve this problem? Well, basically, we know that whatever these two angles are, they have to add up to 90 degrees. So we can set it up just like we set up an equation for complementary angles. So x+x+10=90. Now what we can do is we can just solve this like any other linear equation. I can combine like terms. This ends up being 2x+10 =90. Subtract 10 from both sides over here. We're going to get 2x =80. When you divide by 2 for both sides, what you'll see is that x =40 degrees.
Alright? So x is equal to 40. Are we done here? Is that just the answer? Well, not quite, because the question asks us to find what each of the angles are in the triangle below. It's not enough to find just what x is. Now you actually have to plug it back into those angles to solve for those. Alright? Now for this over here, just because it's x, we actually know that this is already going to be 40 degrees. And then what we can do is we'll say, well, what's x plus 10? That's just going to be 40 plus 10, so in other words, this is 50 degrees. We know these two angles are complementary, 40 and 50. They both add up to 90, so now that's our whole triangle.
Alright? So these are your angles. We have 50 degrees, 40 degrees, and 90 degrees. Alright? All the angles have to add up to 180, and we can use complementary angles to solve for this. Hopefully, that makes sense. Thanks for watching.