1. The problem involves finding the value of the angle labeled \(g\) in a circle with chords intersecting inside and given other angles \(e=31^\circ\) and \(f=40^\circ\).\n\n2. Recall that when two chords intersect inside a circle, the measure of the angle formed between them is half the sum of the measures of the intercepted arcs. Specifically, \(\angle g = \frac{1}{2}(\text{arc opposite to } g + \text{arc adjacent to } g)\).\n\n3. From the image description, angles \(e = 31^\circ\) and \(f = 40^\circ\) represent the intercepted arcs or angles connected to those arcs. Since chords intersect, \(g\) can be found by the formula \(g = \frac{e + f}{2}\).\n\n4. Substitute the given values:\n$$ g = \frac{31 + 40}{2} = \frac{71}{2} = 35.5^\circ $$\n\n5. Therefore, the angle \(g\) is \(35.5^\circ\).\n\n6. This uses the property of intersecting chords and their intercepted arcs in a circle to find the angle measuring the vertex inside the circle.