Question

given the figure below, what is the value of x? 4 14.2 8 6.8

Explanation:

Step1: Use the property of angle - bisector

Since \(NI\) is the angle - bisector of \(\angle KNM\), and \(NK\perp KE\), \(NM\perp MF\), by the angle - bisector theorem (a point on the bisector of an angle is equidistant from the sides of the angle), we have \(NK = NM\).

Step2: Set up the equation

Set \(3x - 4=5x + 12\).
Subtract \(3x\) from both sides: \(-4 = 2x+12\).
Subtract \(12\) from both sides: \(2x=-4 - 12=-16\).
Divide both sides by \(2\): \(x = 8\).

Answer:

\(8\)