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)

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation: