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Question

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

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Solution

Since ABCD is a parallelogram, ADBC

Now,ADBC and transversal AB intersects them at A and B respectively.

A+B=180

Sum of the interior angles on the same side of the transversal is 180

Since ABCD is a parallelogram, ABDC

Now,ABDC and transversal AC intersects them at A and C respectively.

C+D=180

Sum of the interior angles on the same side of the transversal is 180

Now,ADBC and transversal AC intersects them at A and C respectively.

A+D=180

Sum of the interior angles on the same side of the transversal is 180
Now,DCAB and transversal BD intersects them at B and D respectively.

B+D=180

Sum of the interior angles on the same side of the transversal is 180

Hence proved.

1342445_1366007_ans_1c6df47c32d746fa93c4403d29d8df0b.jpg

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