Question

ABCD is a rhombus. Diagonal AC divides it into equilateral triangles. IF ADC = 60°,
find ABC and DCB.​

Answer 1

Answer:

∠DCB =120°

∠ABC=60°

Step-by-step explanation:

In  a rhombus ABCD,AC is a diagonal,which divides rhombus into two equilateral triangle ADC and ABC.

∠ADC=60° [Given]

We know that,

In equilateral ΔADC,

∠ADC+∠DCA+∠CAD=180°

Also,in an equilateral triangle all the three angles are equal.

∠ADC=∠DCA=∠CAD

⇒∠ADC=∠DCA=∠CAD=60°..............(1)

Also,opposite angle of a rhombus are always equal

⇒∠ADC=∠ABC

⇒∠ABC=60°

Now,In equilateral ΔABC,

∠ABC=∠ACB=∠BAC

⇒∠ABC=∠ACB=∠BAC=60°..............(2)

Now,∠DCB=∠DCA+∠BAC

                =60°+60° [From equation (1) and (2)]

         ∠DCB =120°

          ∠ABC=60°

Step-by-step explanation:

Hope this answer will help you.

Answer 2

Answer:

∠DCB =120°

∠ABC=60°

Step-by-step explanation:

In  a rhombus ABCD,AC is a diagonal,which divides rhombus into two equilateral triangle ADC and ABC.

∠ADC=60° [Given]

We know that,

In equilateral ΔADC,

∠ADC+∠DCA+∠CAD=180°

Also,in an equilateral triangle all the three angles are equal.

∠ADC=∠DCA=∠CAD

⇒∠ADC=∠DCA=∠CAD=60°..............(1)

Also,opposite angle of a rhombus are always equal

⇒∠ADC=∠ABC

⇒∠ABC=60°

Now,In equilateral ΔABC,

∠ABC=∠ACB=∠BAC

⇒∠ABC=∠ACB=∠BAC=60°..............(2)

Now,∠DCB=∠DCA+∠BAC

               =60°+60° [From equation (1) and (2)]

        ∠DCB =120°

         ∠ABC=60°

Step-by-step explanation:

Hope this answer will help you.