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: First of all, we need to define what a quadrilateral is. Then we will try to draw the quadrilateral with all the angles as equal and identify the figure.

Complete step-by-step answer:
We are asked to identify a quadrilateral with all angles equal.
A quadrilateral is a figure with four vertices, four angles, four sides and the sum of all the four angles of a quadrilateral is 360°.
Let x be the angle of a quadrilateral. It is given in the question that all the angles are the same.
Therefore, 4x = 360°,
We will now find the quotient of 360 and 4.
Thus, x = 90°
Now, we will draw a figure with all the angles as 90°.

As we can see, if all the angles are 90°, the figure formed is a rectangle or a square. For a rectangle, opposite sides are equal and for a square,

all the sides are equal.
For a trapezium, there is no condition on angles. The only condition is, opposite sides must be parallel.
For a rhombus, all sides are equal and opposite angles are equal.
For a parallelogram, opposite angles are equal and opposite sides are equal.
Thus, option (a) is the correct option.

Note: A quadrilateral should have 4 sides, 4 vertices and 4 angles. These are the only necessary conditions for a figure to qualify as a quadrilateral. If we apply extra conditions, the figure modifies and thus there are special names for these figures.