Question

let ( mangle kijcong mangle jih ),( mangle jih=(4x + 3)^{circ} ),and ( mangle kih=(12x)^{circ} ).( mangle kih=)____(^{circ})

Explanation:

Step1: Use angle - addition postulate

Since \(m\angle KIJ\cong m\angle JIH\), and \(m\angle KIH=m\angle KIJ + m\angle JIH\), then \(m\angle KIH = 2m\angle JIH\).
Given \(m\angle JIH=(4x + 3)^{\circ}\) and \(m\angle KIH=(12x)^{\circ}\), we substitute into the equation: \(12x=2(4x + 3)\).

Step2: Solve the equation for \(x\)

Expand the right - hand side: \(12x=8x + 6\).
Subtract \(8x\) from both sides: \(12x-8x=8x + 6-8x\), which gives \(4x=6\).
Divide both sides by \(4\): \(x=\frac{6}{4}=\frac{3}{2}\).

Step3: Find \(m\angle KIH\)

Substitute \(x = \frac{3}{2}\) into \(m\angle KIH=(12x)^{\circ}\).
\(m\angle KIH=12\times\frac{3}{2}=18^{\circ}\).

Answer:

\(18\)