 Hi, I'm Zor. Welcome to Unizor Education. I will continue solving some little very simple problems related to angles. This is the problem number two. And here is what is necessary to prove. Let's consider you have vertical angles. Let's say this one and this one. What needs to be proven is the following. If you will take a bisector of this angle and bisector of this angle, then these two bisectors form a straight line, which means basically that the angle from here to here is equal to 180 degrees. Well, let's try to basically formulate it in certain language. Acceptable magnetic mutations, EF. Okay, so what's given? Given that angle A O B and angle D O C are vertical. Now, what does it mean that it's vertical? It means that basically, I'll put in parentheses, that B O C is a straight line. So its angle is equal to 100 and H degree. And A O B also is equal to 100 and H degree. That's what it means. And also, given that O E is bisector of angle A O B and O F is bisector of angle C O D. What's necessary to prove that angle E O F equals 180 degree? Well, the proof of this is really much shorter than explanation of all these conditions. It's really a very simple problem. Let's do it this way. Consider this angle is equal to alpha. Then this will be 180 degrees minus alpha since A O D is a straight line. So alpha and 180 minus alpha, they're supplementary to each other. Same thing is here. This is also alpha and this is also 180 degree minus alpha. So let's see what will be if we will start moving from O E to O F. From O E to O F. First we have to cover half of this angle which is 1 half of alpha. Then we have to count all this angle B O D which is 180 minus alpha. And then another half of alpha. And as you see, this is equal to 1 half alpha minus alpha plus 1 half alpha. Only 1 H is remaining. So that's what will be E O F. This is E O F angle equal. Well, that's it. That's the whole proof. As you see, it's very easy problem and I'll try to put some more complex and interesting ones. This is just an illustration of how simple and very effective approach can help in solving some problems. Well, that's it for this problem. Don't forget that Unisor.com website contains lots of educational material which will be helpful in self-study as well as in supervised study. For instance, parents or supervisors want to basically control the educational process of their students and children. There are exams, there are scores which should be presented and there is enrollment basically process. Everything is in there and you're always welcome to try working with this website in a true educational process mode rather than just simply listening to lectures or solving problems. Thank you very much and good luck.