Question

Based on the given information, determine which sides of quadrilateral ABCD must be parallel. angle A=67 B=120 C=73 D=100

Answer 1

D) None of the sides must be parallel.

Answer 2

You have given quadrilateral ABCD with angles m∠A=67°, m∠B=73°, m∠C=120° and m∠D=100°.

m∠A+m∠B=140°,

m∠A+m∠C=187°,

m∠A+m∠D=167°,

m∠B+m∠C=193°,

m∠B+m∠D=173°,

m∠C+m∠D=220°.

If two lines cut by a transversal have supplementary consecutive interior angles (that together form 180°), then the lines are parallel. From the sums above you see that there aren't two quadrilateral angles which form together 180°, so you can conclude that no sides of the quadrilateral are parallel.