Question

what is the value of g? g 47° 31°

Explanation:

Step1: Recall angle - sum property

The sum of angles around a point is 360°. Also, vertical angles are equal. Here, we can consider the fact that the non - overlapping angles adjacent to \(g\) and the vertical angles to them make up a full - turn. Another way is to use the fact that the angles in a linear pair or the angle - sum property of angles formed by intersecting lines. The angles 31° and 47° are adjacent to \(g\) and their vertical angles. The sum of the angles adjacent to \(g\) is \(31^{\circ}+47^{\circ}=78^{\circ}\). Since \(g\) and the sum of these two angles are supplementary (form a straight line, 180°).

Step2: Calculate \(g\)

We know that \(g + 31^{\circ}+47^{\circ}=180^{\circ}\). So, \(g=180^{\circ}-(31^{\circ} + 47^{\circ})\).
\[g = 180^{\circ}-78^{\circ}=102^{\circ}\]

Answer:

\(102\)