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