Given that abcd is a rhombus, what is the value of x?

a.28
b.56
c.48.5
d.18
e.36
f. cannot be determined

Step-by-step explanation:

Given : ABCD is a rhombus and ∠DBC = (5x - 18)°

Let AC and BD intersect each other at O

Now, A rhombus is a parallelogram with opposite sides equal.

⇒ AD ║ BC and AB ║ DC

⇒ ∠CAD = ∠BCA ( Alternate angles are equal)

∴ ∠CAD = ∠BCA = x

Also the diagonals of a rhombus bisect each other at right angles.

⇒ ∠BOC = 90°

Now, in ΔBOC, Using angle sum property of the triangle

∠OBC + ∠BOC + ∠OCB = 180°

⇒ 5x - 18 + 90 + x = 180

⇒ 6x + 72 = 180

⇒ 6x = 108

⇒ x = 18

Therefore, Option D. 18 is correct

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step-by-step explanation: