Question

Prove that adjacent angles of a parallelogram are supplementary.

Answer 1

Answer:

Step-by-step explanation:

IN a parallelogram ABCD    

opposite angles are equal

                    ∠A=∠C  and ∠B =∠D

sum of 4 angles   = 360

   ∠A   + ∠B+∠C + ∠D =360

    ∠A   + ∠B+∠A + ∠B =360

       2[∠A   + ∠B]  =360

             ∠A   + ∠B =  180

Answer 2

Prove that adjacent angles of a parallelogram are supplementary.

As we know opposite angles are equal and sides are parallel.

So if ABCD is a llgm.

Angle B = angle D,

Angle A = angle C

=) A+B = C+D,

Sum of all angles of a parallelogram = 360°

=) A + B + C + D = 360°

=) 2(A+B) = 360°

=) A+B = 180°

Or

=) 2(C+D) = 360°

=) C+D = 180°.