Question

PQRS is a rhombus such that one of its diagonals PR is equal in length to its sides. Which of the following gives
the four angles of the rhombus?

Option 1. 60°, 60°, 60°, 60°
Option 2. 120°, 120°, 120°, 120°
Option 3. 90°, 90°, 90°, 90°
Option 4. (Such a rhombus with a diagonal equal to the sides is not possible)​

Answer 1

my option is not available

let sides of a rhombous be a

then, as per question, one diagonal is also equal to a

diagonals of a rhombous are perpendicular bisectors

(I am not able to make diagram here)

imagine a right angle triangle inside rhombous.

the hypotenuse is a ( side of rhombous)

one side is a/2 ( half of one diagonal)

other side = √ a^2 - ,(a/2)^2

= √3a^2/4

= √3a/2

this length of other diagonal is 2*√3/2a = √3a

now tan any acute angle will be either

√3a/2/a/2

= √3 or 1/√3

the acute angles will be 60° and 30°

repeating this procedure in any adjacent triangle, we can derive that two opposit angles will be 120° each and other two angles will be 60° each.

so angles will be

120,60,120,60

but the option is not available