Question

Which of the following statement(s) is/are
true ?
(A) A parallelogram in which two adjacent angles are equal is a rectangle.
(B) A quadrilateral in which both pairs of opposite angles are equal is aparallelogram.
(C) In a parallelogram the number of acute angles is two.
(D) All the above.​

Answer 1

Answer:

(A) True

If a parallelogram ABCD has equal adjacent angles, then A=B. But, we know that A=C and B=D(since, opp. angles are equal).

So, A=B=C=D=90°

And a parallelogram with all angles equal is a rectangle

Hence, it's true.

(B) True. Since the parallelogram has an exclusive property of having both pairs of opposite angles equal.

(C) True. Some none of the angles is equal to 90° in a parallelogram, and the adjacent angles have sum equal to 180°, so one of the angles is necessarily acute and other, obtuse between the two angles, and in 4 angles, two are acute.