Question

One of the diagonals of a rhombus is equal to one of its sides. Find the angles
of the rhombus.​

Answer 1

Answer:

60° , 120° , 60° , 120°

Step-by-step explanation:

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Answer 2

Answer:

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