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.

Answer 1

so opposite angles are equal

that means

angle A = angle C

angle B = angle D

Answer 2

angle A is 100 - x
angle C is 110 - 3x

so set them equal to each other and solve for x

100 - x = 110 - 3x

Answer 3

5

Answer 4

Good! And similarly

angle B = angle D

80 + x = 75 + 2x

Answer 5

Same thing

Answer 6

Exactly! So we found the value of x to prove that the quadrilateral is a parallelogram