Question

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

Answer 1

5x - 18 + x = 90

6x = 108

x = 18 degrees

Answer 2

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