In quadrilateral ABCD, m< ACD = 2x + 4 and m< ACB = 5x - 8. For what value of x is ABCD a rhombus?

x = 4

Step-by-step explanation:

If a quadrilateral is a rhombus, then the diagonals of it will bisect each angle of the quadrilateral.

Now, the diagonal AC bisects angle C into ∠ ACD and ∠ ACB.

Hence, ∠ ACD = ∠ ACB

⇒ 2x + 4 = 5x - 8 {Given that ∠ ACD = 2x + 4 and ∠ ACB = 5x - 8 }

⇒ 3x = 12

⇒ x = 4 (Answer)