Question

look at the diagram.
which equation can be used to solve for x?
3x + 45 = 180
6x + 42 = 180
3x + 51 = 180
6x + 48 = 180
solve for x.
x =
submit
work it out

Explanation:

Step1: Find the sum of angles

Since \( \angle FGD = 90^{\circ}\) and \( \angle DGE = 48^{\circ}\), then \( \angle FGE=90^{\circ}- 48^{\circ}=42^{\circ}\).
The sum of \( \angle CGF=(3x + 3)^{\circ}\) and \( \angle FGE = 42^{\circ}\) is \(3x+3 + 42\).

Step2: Set up the equation

Because \( \angle CGE\) is a straight - angle (\(180^{\circ}\)), we have the equation \(3x+3 + 42=180\), which simplifies to \(3x + 45=180\).

Step3: Solve the equation

Subtract \(45\) from both sides: \(3x=180 - 45\), so \(3x = 135\).
Divide both sides by \(3\): \(x=\frac{135}{3}=45\).

Answer:

\(x = 45\)