 In this video we're going to just do a couple of example problems using rectangles. So we are given here that quadrilateral math is a rectangle and they tell us that Tk is 2x plus 3 and Ka is 5x minus 9. Well because this is a rectangle we know that the diagonals bisect each other. So therefore Tk and Ka have to be congruent. To do this problem we're just going to set 2x plus 3 equal to 5x minus 9 and we're going to solve for x. So I'm going to subtract 2x on both sides and I'm going to add 9 on both sides and when we divide both sides by 3 we get x equals 4. Now I'm going to use that to find mk. Well because mk is a portion of a diagonal we know because the diagonals bisect each other and we also know in a rectangle that the diagonals are congruent that means that all of these pieces have to be congruent. So therefore if I plug 4 back in to either Tk or Ka I will be able to find mk. So I'm just going to go ahead and do 2 times 4 and add 3 and so mk would equal 8 plus 3 which is 11. In this example we are working with angles and so we see that we are given the measure of angle m at so that's this angle right here and that's equal to 2x squared plus 2 and they tell us that the angle measure of TAH which is this angle is equal to 14x. Well what we know because this is a rectangle we know that the angles m, a, h and t have to be 90 degree angles. So what we are going to do is we are going to add these two measures together and set them equal to 90. So 2x squared plus 2 plus 14x has to equal 90 and in order to solve this we have to think back to the algebra unit that we just finished and notice that we have both an x squared term and an x term. So the only way of solving this is to use factoring. Well in order to use factoring to solve it has to be equal to zero. So the first thing that we are going to do is subtract the 90 make sure you subtract it on the like term and I am going to write it in my answer in standard form. So 2x squared plus 14x minus 88 equals zero. Now I am going to move my screen up a little bit here and the next thing we are going to do is factor and hopefully you recognize that there is a GCF, a common factor that we can factor out and that is 2 and if we factor out 2 what is left is x squared plus 7x minus 44 and so then I am going to factor that trinomial and so in order to factor the trinomial we need what two numbers multiply to negative 44 and add to 7. So hopefully you are able to come up with 11 and negative 4 and then remember to solve you just set your factors equal to zero and so we get two answers. x equals negative 11 and x equals 4. Well here is the point in the problem where we have to remember that we are dealing with angle measures and if I were to plug negative 11 back in here for x I would get a negative angle measure for angle tAH and that doesn't make any sense. So what we are going to do in this case is we are going to ignore that negative 11 because it doesn't make sense for this problem. So we would just give our answer as x equals 4.