Question

1. look at the diagram. diagram: horizontal line with points f (left), g (center), c (right); point a above g, point d below g. angle between fg and ag is 60°, angle between cg and dg is 3(5 + x)°. which equation can be used to solve for x? options: 3(5 + x) = 60; 3(5x) + 60 = 90; 3(5x) = 60; 3(5 + x) + 60 = 180. solve for x. x =

Explanation:

Part 1: Determine the correct equation

Step1: Identify angle relationship

Angles on a straight line sum to \(180^\circ\). The \(60^\circ\) angle and \(3(5 + x)^\circ\) angle are supplementary (form a straight line at point \(G\)).

Step2: Form the equation

So, their sum should be \(180^\circ\), giving \(3(5 + x)+60 = 180\).

Step1: Subtract 60 from both sides

\(3(5 + x)+60 - 60=180 - 60\)
\(3(5 + x)=120\)

Step2: Divide both sides by 3

\(\frac{3(5 + x)}{3}=\frac{120}{3}\)
\(5 + x = 40\)

Step3: Subtract 5 from both sides

\(5 + x-5 = 40 - 5\)
\(x = 35\)

Answer:

\(3(5 + x)+60 = 180\)

Part 2: Solve for \(x\)