 Hello and how are you all today? The question says find the values of the angles x, y and z in each of the following. We are dealing with the second part here. We need to find out the value of x, y and z and we are given the measurement of these two angles as 40 degrees and 25 degrees respectively. Now let us quickly proceed with the solution. Now here we are given this angle as 40 degrees. If we look directly opposite to this angle we have z and we can see that this line and this line is getting intersected at this point. So angle z will be equal to 40 degrees with the reason that it is forming a vertically opposite angle and vertically opposite angles are equal to each other. Here through with angle z now let's proceed on with angle y. Now we can see that angle y plus angle z is forming a linear pair. So their sum will be equal to 180 degrees. We already have the value of z as 40. So we have y plus 40 degrees equal to 180 degrees or we have y as 180 degrees plus 40 when taken from left-hand side to right-hand side will become minus 40 and we have y as 140 degrees. Now we can see that angle y is vertically opposite to this angle which is the sum of x and 25. So we can see that y is equal to x plus 25 degrees being vertically opposite, isn't it? We have the value of y as 140 degrees. So we have 140 degrees equal to x plus 25 degrees. We need to find the value of x. So transposing 25 degree from right-hand side to left-hand side and changing its sign will be 140 degree minus 25 degree equal to x that is equal to 115. So the value of x is 115. So let me write down all the answers one again. So we have x as 115 degrees, y as 140 degrees and z as 40 degrees. Right, this completes the solution. Hope you understood the solution well and enjoyed it. Bye.