given that ABCD is a rhombus, what is the value of x?​

Accepted Solution

Answer:D. 18Step-by-step explanation:We know:1. Diagonals of a rhombus are perpendicular.2. Diagonals divide the rhombus on four congruent right triangles.3. The sum of measures of acute angles in a right triangle is equal 90°.Angles CAD and ACB are alternate angles. Therefore they are congruent:m∠DAC = m∠ACB ⇒ m∠ACB = x°.From 3. we have the equation:(5x - 18) + x = 90(5x + x) - 18 = 90              add 18 to both sides6x = 108             divide both sides by 6x = 18