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10 March, 11:57

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°

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  1. 10 March, 12:26
    0
    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
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