Question

m ∠ A = 100 - x
m ∠ B = 80 + x
m ∠ C = 110 - 3x
m ∠ D = 75 + 2x
Quadrilateral ABCD is a parallelogram if both pairs of opposite angles are equal. Prove that Quadrilateral ABCD is a parallelogram by finding the value of x.
A) x = 5
B) x = 7
C) x = 10
D) x = 15/2

Answer 1

<A must be congruent to <C

100 - x = 110 - 3x

100 + 2x = 110

2x = 10

x = 5

m<A = 100 - x = 100 - 5 = 95

m<C = 110 - 3x = 110 - 3 * 5 = 110 - 15 = 95

Opposite angles A and C are congruent.
Now we need to check opposite angles B and D.

m<B = 80 + x = 80 - 5 = 75

m<D = 75 + 2x = 75 + 2 * 5 = 75 + 10 = 85

Opposite angles B and D are also congruent.

Answer: x = 5