Question

ABCD is a rhombus. Diagonal AC divides it into equilateral triangles. FADO = 60
find ZABC and _DCB.​

Answer 1

Answer:

Let ABCD is a rhombus. AC and BD are diagonals such that, AC is equal to all sides of rhombus.

⇒ AB = BC = CD = DA = Diagonal AC.

⇒ In △ABC,

⇒ AB = BC = AC [Given]

∴ △ABC is an equilateral triangle.

⇒ So, ∠CAB = ∠ABC = ∠ACB = 60

∘

[Angles of equilateral triangle] --- ( 1 )

⇒ Similarly, in △ADC we get,

⇒ ∠CAD = ∠ADC =∠ACD = 60

∘

----- ( 2 )

⇒ ∠BAD = ∠BAC + ∠CAD = 60

∘

+ 60

∘

= 120

∘

-- ( 3 )

⇒ ∠BCD = ∠BCA + ∠ACD = 60

∘

+ 60

∘

= 120

∘

---- ( 4 )

So, from ( 1 ), ( 2 ), ( 3 ) and ( 4 ) we get,

The angles of a rhombus ABCD are 120

∘

,60

∘

,120

∘

,60

∘

.