 Welcome again guys to another session on quadrilateral and now let us understand a very important property of Quadrilateral and that is angle some property of a quadrilateral So while dealing with triangles you would have seen or you would have gone through the similar property where in What was angle some property of a triangle so angle some property of a triangle was that some of some of all or all the three some of all the three angles of a Offer triangle was equal to 180 degrees. This was nothing but this was angle some property Angle some property of Our triangle is it it? Now we are going to study angle some property of a quadrilateral So you know that there are four angles in a quadrilateral and that is angle a angle B Angle C and angle D. These are four angles in a quadrilateral. So the angle some property states that sum of sum of the four Angles so when we say four angles we mean four interior angles of a quadrilateral quadrilateral is equal to 360 degrees so in terms of radians we can call it as two by Radiant okay, so now let us understand How do we arrive at this so hence let's try to prove this property? So what we'll do is we will use angle some property for triangle to prove angle some property of a quadrilateral So let's do a construction so construction. We have to do a construction here So since we are going to use angle some property of a triangle, so let's make two triangles out of here So hence I join B and D Are joined so the diagonal B and D is what a diagonal? It's a diagonal isn't it B and D B D basically is a diagonal So I joined any of the diagonals again you could have joined AC as well There's no problem there and the proof remains the same so hence now we can say that and Before that let us name the angles for our ease of writing So let's say this is one this angle let it be two then this angle let it be three This angle let it be four This one to be five and this one to be six Okay, so hence we can say angle one Plus angle two plus angle six is equal to 180 degrees or pi radians, right? And this is because of angle some Angle some property Angle some property of a triangle isn't it angle some property if you triangle Similarly, I can write angle three plus angle four plus angle five This is also 180 degrees same property so you can write angle some property of a triangle now Let this be equation one and let this be equation two And now what I'm going to do is I'm going to do one and two addition one plus two Let's add one plus two So what would you get you will get angle one on the LHS angle one plus angle two plus angle six plus angle three plus angle four plus angle five is equal to 360 degrees 180 plus 180 in the RHS will give you 360 Now if you club them together you will get angle one plus angle two plus angle three So I am clubbing them together and then angle four and then angle five plus angle six Clubbing them together. Let's go back to the figure. So if you see here Clearly here angle two and angle three. Can you see angle two plus angle three is D? Isn't it an angle? Five plus angle six here angle five plus angle six is angle B So hence I can say angle one is nothing but angle a Angle two plus three can be written as angle B and angle four is angle C and five plus six is angle B and this all is 360 degrees, so if you see a B C and D all put together is 360 degree hence proved Right so angle some property of a quadrilateral says that the sum of all the interior angles of a quadrilateral Will be equal to 360 degrees. You know how you have to remember this theorem or this property You know because We are going to use this property again and again and after this session We are going to solve some problems based on this particular property. Thank you