Question

given rhombus ijkl below, m∠klm = 57°. if m∠ilm = (4x + 5)°, solve for x.

Explanation:

Step1: Use the property of rhombus diagonals

In a rhombus, the diagonals bisect the angles. So, \(m\angle ILM=\frac{1}{2}m\angle KLM\).

Step2: Substitute the given values

Since \(m\angle KLM = 57^{\circ}\) and \(m\angle ILM=(4x + 5)^{\circ}\), we have the equation \(4x+5=\frac{1}{2}\times57\).
First, calculate \(\frac{1}{2}\times57 = 28.5\). Then the equation becomes \(4x+5 = 28.5\).
Subtract 5 from both sides: \(4x=28.5 - 5\). So, \(4x=23.5\).
Divide both sides by 4: \(x=\frac{23.5}{4}=5.875\).

Answer:

\(x = 5.875\)