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.