M∠a = 100 + 5x m∠b = 77 − 4x m∠c = 106 + 3x m∠d = 47 + 6x quadrilateral abcd is a parallelogram if both pairs of opposite angles are congruent. prove that quadrilateral abcd is a parallelogram by finding the measures of the opposite angle pairs? a) 95°, 85° b) 105°, 75° c) 115°, 65° d) 125°, 55°

C)115°, 65°

Step-by-step explanation:

A and C are opposite angles

A = C

100 + 5x = 106 + 3x

Subtract 3x from each side

100 + 5x-3x = 106 +3x-3x

100 + 2x = 106

Subtract 100 from each side

100-100 + 2x = 106-100

2x = 6

Divide by 2

2x/2 =6/2

x=3

Angle A = 100+ 5x

               =100 + 5(3)

               = 100+15

               = 115

Angle C = 115

Angle B = 77 - 4x

              = 77 -4(3)

              = 77-12

              = 65

e) none of the above because the measure of angle cba is 101°

y = 0.77(x)

step-by-step explanation:

the jacket retains this value after 23% cut or retains 77% of original value. plug original 87 jacket price for x and the remaining value should be y.