Question

17. ABCD is a shombus . find the value of x. A=36, D=x ​

Answer 1

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

Answer 2

Answer:

Step-by-step explanation:

 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