In a parallelogram ABCD, prove that the sum of any two consecutive angles is 180o.

Asked by Topperlearning User | 9th Dec, 2013, 01:40: AM

Expert Answer:

ABCD is a parallelogram, therefore AD||BC
Now, AD||BC and transversal AB intersects them
A + B = 180o               (sum of interior angles on the same side of transversal)
Similarly you can prove that
B + C = 180o, C + D = 180o and D + A = 180o 

Answered by  | 9th Dec, 2013, 03:40: AM