Question

PQRS is a cyclic quadrilateral, in which if $\angle P-\angle R={30}^o$ and $\angle Q-\angle S=-{30}^o$, then PQRS is a

• A. parallelogram
• B. rhombus
• C. square
• D. trapezium

Answer 1

The correct option is D trapezium

Any four-sided figure (quadrilateral) whose four vertices (corners) lie on a circle.

• The sum of opposite angles of a cyclic quadrilateral is 180 degrees.
• According to the properties of cyclic quadrilateral, every cyclic parallelogram is a rectangle and every cyclic rhombus is a square.

And in the given question, difference between the angles are given, which is not possible for square and rectangle. It not possible to have given condition in Option A,B,C . So, the correct answer is option D.