Question

look at the diagram.
which equation can be used to solve for x?
solve for x.
x =

Explanation:

Step1: Find the equation

Since \( \angle BGD = 180^{\circ}\) (a straight - line angle), and \( \angle BGC+\angle BGF+\angle FGE = 180^{\circ}\). Given \( \angle BGC = 122^{\circ}\), \( \angle BGF = 42^{\circ}\), \( \angle FGE=(8x)^{\circ}\). The equation is \(8x + 42=122\) (vertical - angle relationship: \( \angle BGC\) and \( \angle BGF+\angle FGE\) are related as \( \angle BGC\) and \( \angle BGF+\angle FGE\) form a linear - pair with the other angles around point \(G\), and using the property that the sum of angles on a straight line is \(180^{\circ}\), but more simply by vertical - angle and adjacent - angle relationships).

Step2: Solve the equation \(8x + 42=122\)

Subtract \(42\) from both sides:
\(8x+42 - 42=122 - 42\)
\(8x = 80\)
Divide both sides by \(8\):
\(x=\frac{80}{8}\)

Answer:

\(x = 10\)