Question

ABCD is a quadrilateral such that every pair of adjacent angles are supplementary (their sum is 180 ). Prove that ABCD is a parallelogram.

Answer 1

- If angle A is supplementary to angle B, then angle A=180-angle B

- If angle B is supplementary to angle C, then angle C=180-angle B

- For the first 2 arguments we have angle A=angle C

-If angle C is supplementary to angle D, then angle D=180-angle C

- If angle B is supplementary to angle C, then angle B=180-angle C

- For the last two arguments we have angle B=angle D

If angle A=angle C and angle B=angle D the quadrilateral ABCD is a parallelogram