Question

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°

Answer 1

The measure of the quadrilateral depends...

Parallelogram = B. 65 degrees

Trapezoid = C. 115 degrees

Answer 2

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.