Question

one of the diagnoals of a Rhombus is equal to one of its sides find the angle of rhombus​

Answer 1

Answer:

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Step-by-step explanation:

ABCD is a rhombus.

⇒60⁰,120⁰,60⁰,120⁰

Answer 2

Answer:

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Step-by-step explanation:

ABCD is a rhombus.

⇒AC=BC ____(1)(given)

BC=AB ___(2)(side of rhombus)

From eqns(1) and (2)

AC=BC=AB

⇒△ABC is equilateral triangle.

So, ∠ABC=60°

∠BCA=60°

____(3)

∠CAB=60°

____(4)

Similarly, in △ADC,AD=DC(sides of a rhombus)

AD=BC

But BC=AC

∴AD=AC

∴AD=DC=AC

∴DAC is an equilateral triangle.

⇒∠CAD=60°

___(5)

⇒∠ADC=60°

⇒∠DCA=60°

___(6)

From eqns(3) and (6) we get

∠BCA+∠DCA=60°+60°=120°

∴∠C=120°

From eqns(4) and (5),

∠CAB+∠CAD=60°+60°=120°

∴∠A=120°

Hence the four angles of the Rhombus are 120°,60°,120°,60°