Question

M∠A = 75 + 5x

m∠B = 111 − 6x

m∠C = 87 + 3x

m∠D = 39 + 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°

Answer 1

Answer:

See below

Step-by-step explanation:

For a parallelogram m < A = m < C so:-

75 + 5x = 87 + 3x

2x = 12

x = 6  

and m< A = 75 + 30 = 105

and m < C = 87 + 18 = 105

Now if the other 2 angles are  = 75 degrees( that is the same side angles add up to 180 degrees) we have proved that it is a parallelogram.

m < B = m < D

111 - 6x = 39 + 6x

-12x = -72

x = 6

m < B = 111 - 36 = 75 and m < D = 39 + 36 = 75

So this has been proved.