Question

in a Parallelogram ABCD , prove that sum of any two consecutive angles os 180 °​

Answer 1

Answer:

yes.in a parelellogram sum of adjacent angles is 180.

Answer 2

Answer:

Since ABCD is a parallelogram, AD∥BC

Now,AD∥BC 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, AB∥DC

Now,AB∥DC 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,AD∥BC 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,DC∥AB 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.

solution