Question

In a parallelogram ABCD if one angle has 24 less than twice the smallest angle, find the measures
of all angles of a parallelogram ABCD.

Answer 1

In the parallelogram ABCD
                         angle A+angle B= angle C + angle D= 180
                   Let angle A=x
                   then angle B= 2x-24
           We have x+2x-24=180
                                   3x= 204 ⇒x=68         
                         Angle B= 68*2-24=112
Hence the angles are 68,112,68 and 112.

Answer 2

Let smaller angle be x Then 2nd angle = 2x -24 In parallelogram, The angle opposite to each other are equal and sum of all angles= 360 Then. - ( 2x -24)+(2x-24)+x + x= 360 2x + 2x + x + x- 48= 360 6x-48=360 6x=360+48 6x=408 X=408÷6 X= 68 And the other = (68×2)- 24= 112