What values of a and b make quadrilateral MNOP a parallelogr

What values of a and b make quadrilateral MNOP a parallelogram given the length of MN=4a-12, NO=2b+8, OP=3a-6, and PM=5b-1?

Solution

In a Parallelogram, opposit sides are equal. Therefore in a parallelogram MNOP, MN = OP and NO = PM

MN = OP; 4a - 12 = 3a - 6, Solving 4a-3a = -6+12, Therefore a = 6

NO = PM; 2b + 8 = 5b - 1, Solving 8+1 = 5b-2b , 3b = 9 and Therefore b = 3