Question

All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?
A. Rectangle
B. Trapezium
C. Rhombus
D. Parallelogram

Answer 1

Hint: We write definitions of each of the given quadrilaterals and check which of the given polygons are quadrilateral. Then we check which polygon has all its angles equal using the definitions.

Complete answer:
We know a quadrilateral is a closed figure having four vertices (corners) and four edges (sides).
Now we define rectangles, trapezium, rhombus and a parallelogram using the characteristics of quadrilaterals.
Rectangle: A rectangle is a quadrilateral having all angles as right angles and opposite sides equal and parallel to each other. A rectangle is a quadrilateral with all angles equal.
Trapezium: A quadrilateral having one pair of opposite sides parallel and one pair of opposite equal sides is called a trapezium. Since we have two sides that are not equal and two sides that are not parallel, the angles can never be equal. A trapezium is a quadrilateral but does not have all angles equal.
Rhombus: A rhombus is a quadrilateral whose all sides are of equal length and opposite sides are parallel to each other. Opposite angles of rhombus are equal in measure. A rhombus is a quadrilateral but not all angles are equal.
Parallelogram: A parallelogram is a quadrilateral having the opposite pair of sides equal and parallel. The angles opposite to each other are equal in measure. A parallelogram is a quadrilateral but not all angles are equal.

Option A. is correct.

Note: Many students make the mistake of writing the correct option as a parallelogram as they think opposite sides are parallel and equal so opposite angles are also equal. But we don’t have all sides equal and all angles equal in this case, so parallelogram is not the correct option.