Question

If the ratio of angles (taken in order) of a quadrilateral is 1 : 2 : 3 : 4, then it could be a:

• A. parallelogram
• B. cyclic quadrilateral
• C. kite
• D. trapezium

Answer 1

The correct option is B

cyclic quadrilateral

If we assume the angles to be 1x, 2x, 3x, and 4x; we can see that 1x + 4x = 2x + 3x = 5x. So, 1x and 4x will add up to ${180}^{\circ }$ and 2x and 3x will also add up to ${180}^{\circ }$. Since the sum of opposite angles is ${180}^{\circ }$, thus we can conclude that one pair of opposite sides will be parallel. Hence, it is a cyclic quadrilateral.