Question

Is quadrilateral $ABCD$ a parallelogram, if $\angle A={70}^{\circ }$ and $\angle C={65}^{\circ }$? Give reason.

Answer 1

Answer: Quadrilateral ABCD is not a parallelogram.

In a parallelogram, the opposite angles must be equal.

So, if ABCD is indeed a parallelogram, then angle A and angle C being opposite angles must be equal.

However, as stated in question, angle A = 70 degrees

and angle C = 65 degrees.

Thus angle A and angle C are not equal.

Hence, the condition that opposite angles must be equal is not met. Hence there is a contradiction to our assumption. Hence, quadrilateral ABCD is not a parallelogram.