Question

In a parallelogram, if each angle is equal, then it is called.
A) Rectangle
B) Square
C) Rhombus
D) None of these

Answer 1

Hint: First find the measure of each angle of the parallelogram using the condition that the measure of each angle is equal and then use the property of parallelogram to find the required result.
In any parallelogram, if all the angles are equal then they must be of $90^\circ $ or we can say that all angles must be right angles because the sum of all the angles of a parallelogram is 360 degree.

Complete step-by-step answer:
We have given a parallelogram having each angle equal to each other and we have to find whether it is rectangle, square, rhombus, or none of them.
Firstly, we know that the sum of all angles of a quadrilateral is $360^\circ $.
Now, assume that each angle of the rectangle is $x$, then using the property of sum of angles of quadrilateral:
$x + x + x + x = 360^\circ $
$4x = 360^\circ $
$x = 90^\circ $
So, the measure of each angle of the quadrilateral is $90^\circ $.
Now, in a parallelogram, the opposite sides are equal and parallel to each other and we have each angle of $90^\circ $.
Take a look at the figure that has all these properties:

So, a rectangle satisfies all these given conditions because in a rectangle each angle is a right angle and opposite sides are equal and parallel to each other.
So, rectangles satisfy these given conditions in all forms.

Therefore, the correct option for the answer is option A which is a rectangle.

Note: In this problem, we cannot take square because it may satisfy the condition given that right and parallel and equal opposite sides but for square, we need one more condition which is all the sides must be equal to each other.