In a parallelogram `A B C D ,` prove that sum of any two consecutive angles is `180^@`

Explanation

To prove: Sum of any two consecutive angles is `180^@`.
`ABCD` is a parallelogram
`therefore AD` parallel to `BC` and `AB` parallel to `CD`
Now, `AD` is parallel to `BC` and transversal `AB` intersects them
`therefore angleA+ angleB=180^@` (sum of interior angles on the same side of transversal)
Similarly we can prove that
`angleB+angleC=180^@`, `angleC+angleD=180^@` and `angleD+angleA=180^@`.
Hence Proved.