Answer:
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
