Quadrilateral abcd is a parallelogram if both pairs of opposite angles are congruent. prove that quadrilateral abcd is a parallelogram by finding the measures of the opposite angle pairs? a) 95°, 85° b) 105°, 75° c) 115°, 65° d) 125°, 55°

5°

As you have written quadrilateral abcd is a parallelogram if it's opposite angles are congruent.

So we have to find the measure of opposite pair of angles.

I have drawn four parallelograms

A)95°, 85°

∠a+ ∠b=180°

∠a = ∠c =95°

∠b = ∠d =85°

2.  b)105°, 75°

∠a = ∠c =105°

∠b = ∠d =75°

c). 115°, 65°

∠a = ∠c =115°

∠b = ∠d =65°

D) 125°,55°

∠a = ∠c =125°

∠b = ∠d =55°

     In all the four cases

            ∠a+ ∠b=180°

           ∠b + ∠c=180°

          ∠c  + ∠d =180°

         ∠d +   ∠a=180°

and in all cases   ∠a=∠c    , ∠b=∠d

as sum of interior angles on same side of transversal is 180° so opposite sides become parallel.If in a quadrilateral opposite sides are parallel then it is a parallelogram.

So we can say that quadrilateral abcd is a parallelogram.

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