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If one angle of a parallelogram is $90 °,$ then the parallelogram is called a

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Kite

Rectangle

Rhombus

None of these

answer is B.

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Detailed Solution

Given that one angle of a parallelogram is

90 ° .

Consider that ABCD is a parallelogram.
Question Image

Using the parallelogram property, we have,

A B | | C D and A D | | B C

It is given that one angle of a parallelogram is

90 ° .

Let’s say

∠ A = 90 ° .

Using the adjacent angles property, we have,

⇒ ∠ D = 180 ° − ∠ A ⇒ ∠ D = 180 ° − 90 ° ⇒ ∠ D = 90 °

We know that opposite angles of parallelogram are equal.
Therefore, we have,

∠ D = ∠ B and ∠ A = ∠ C

⇒ ∠ A = ∠ B = ∠ C = ∠ D = 90 °

We know that, when all four angles of a parallelogram are right angles, the parallelogram is called a rectangle.
Therefore, if one angle of a parallelogram is

90 °,

then the parallelogram is called a rectangle.
Hence, option (2) is correct.

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