Question

find the range of values for x. 48° (2x - 12)° 22 16 ? < x <

Explanation:

Step1: Apply the triangle - inequality theorem for angles

In a triangle, the measure of an angle must be greater than 0. So, \(2x - 12>0\).
\[2x-12 > 0\]
\[2x>12\]
\[x > 6\]

Step2: Consider the upper - bound of the angle

The sum of angles in a triangle and the relationship between angles in the given figure. Also, note that the angle \(2x - 12\) must be less than \(48\) (by the properties of the angles in the non - overlapping triangles formed). So, \(2x-12<48\).
\[2x-12 < 48\]
\[2x<48 + 12\]
\[2x<60\]
\[x<30\]

Answer:

\(6