Question

In ABCD is a rhombus, seg BD is the diagonal. If ∠ABD = 37° then find ∠DBC

Answer 1

Answer:

Please match your answer

Step-by-step explanation:

Understanding Quadrilaterals

Parallelogram

The diagonals AC and BD of ...

The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O.

If ∠DAC=32

o

and ∠AOB=70

o

, then ∠DBC is equal to?

In given figure,

Quadrilateral ABCD is a parallelogram.

So, AD ∣∣ BC

∴ ∠DAC = ∠ACB --- ( Alternate angle)

∴ ∠ACB = 32

∘

∠AOB + ∠BOC = 180

∘

--- (straight angle)

⇒70

∘

+ ∠BOC = 180

∘

∴ ∠BOC = 110

∘

In △BOC,

∠OBC + ∠BOC + ∠OCB = 180

∘

⇒∠OBC + 110

∘

+ 32

∘

= 180

∘

⇒ ∠OBC = 38

∘

∴ ∠DBC = 38

∘

solution

Answer 2

ABCD is our rhombus with the diagonals

AC=24 cm and BD=70 cm respectively.

Now, since a rhombus is also a parallelogram, the diagonals bisect each other at the point where they meet, which in this case is O.

Therefore,

OC=OA=AC/2=24/2=12 cm and OB=OD=BD/2=70/2=35 cm.

Now, in a rhombus the diagonals intersect each other at 90 degrees.

Hence, ∠BOC=90^o

In right angled triangle BOC, applying the Pythagoras' theorem, we have:

BC=√OB^2+OC^2

⇒BC=√35^2+12^2

⇒BC=√1369

⇒BC=37 cm

Now, in a rhombus, the length of all sides are equal i.e. AB=BC=CD=DA

Thus perimeter = 4⋅(BC) = 4⋅37 = 148 cm.