 Hello and welcome to the session. In this session we discussed the following question which says if one angle of a parallelogram is 24 degrees less than twice the smallest angle, find the largest angle of the parallelogram. First let's recall the fact that is the sum of the adjacent angles of a parallelogram is 180 degrees. This is the key idea for this question. Let's move on to the solution. Consider this A, B, C, D is a parallelogram we take let angle A be smallest angle the parallelogram A, B, C, D and we take angle A be equal to x degrees that is we have this angle is x degrees by the question we have that one angle is 24 degrees less than twice the smallest angle so we take let angle B is equal to 2x minus 24 degrees that is the angle is 24 degrees less than twice the smallest angle which is x degrees so this angle B is 2x minus 24 degrees now from the figure you can see that angle A and angle B are adjacent angles of parallelogram A, B, C, D so we have angle A plus angle B is equal to 180 degrees since the sum of adjacent angles of a parallelogram is 180 degrees now substituting the values for angle A and angle B we get x degrees plus 2x minus 24 degrees is equal to 180 degrees that is we have x degrees plus 2x degrees minus 24 degrees is equal to 180 degrees this further gives us 3x degrees is equal to 180 degrees plus 24 degrees and this is equal to 204 degrees so this means that x degrees is equal to 204 degrees upon 3 which is equal to 68 degrees now since we have taken angle A that is x degrees to be the smallest angle so obviously 2x minus 24 degrees that is angle B would be the largest angle so the largest angle as the parallelogram A, B, C, D is angle B that is 2x minus 24 degrees now putting the value for x that is 68 in this we get 2 into 68 minus 24 degrees this is equal to 136 minus 24 degrees equal to 112 degrees so we have angle B is equal to 112 degrees so our final answer is the largest angle of the parallelogram of measure 112 degrees so this completes the session hope you understood the solution for this question