Question

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°

Answer 1

B) 105, 75

Explanation:

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Answer 2

C) 115°, 65°

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