Question

In the figure ,ABCD is a rhombus. find the value of X and Y .

Answer 1

Answer:

In a rhombus diagonals bisect the angles and the opposite angles measure the same . In a rhombus all sides measures the same 

so, 

     in 1)  in ΔABC

  

                ∠CAB = ∠BCA = 40

               ∠CAB+∠BCA+∠ABC= 180

                80 +∠ ABC = 180

                ∠ABC = 100

as we know that the diagonals of a Rhombus bisect the angles

                     ∠ABC/2 = x = 50

as we know that opposite angles of a rhombus are equal 

y = 50

2) ∠DAC=∠DCA=62

∠DAC/2= ∠DCB/2 = x = 31

 ∠CAB+∠ACB+∠ABC = 180

62 + ∠ABC = 180

∠ABC= 118

∠ABC/2 = y = 59

similarly in 3)

 ∠ABC=∠ADC

AB = BC

so, ∠BAC =∠ACB= y 

∠BAC+∠ACB +∠ABC = 180

2y + ∠ABC = 180

2y + 120 = 180

2y = 60

y = 30

 as we know the diagonals bisect the angles so X=Y

x=y=30