This is a triangle with an inequality involving an angle $(2x + 6)^\circ$. Let's solve it step by step.

Step 1: Recognize the triangle inequality

In a triangle:

1. The sum of the angles must equal $180^\circ$.
2. Each angle must be greater than $0^\circ$.
3. Additionally, the given diagram implies this inequality: $2x + 6 > 0$ because all angles must be positive.

Step 2: Set up the angle sum equation

The given angles are: $(2x + 6)^\circ, 34^\circ, \text{ and the third angle}.$ From the triangle sum rule: [ (2x + 6) + 34 + \text{third angle} > to calc