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