Question

one of the angle of a rhombus and its sides are equal. find the angles of the rhombus​

Answer 1

Answer:

use its identity and resolve it

Answer 2

Answer:

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)

  ..........(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  

∘