Question

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

Explanation:

Step1: Analyze the right - angle

Since \( \angle FGD = 90^{\circ}\), and \( \angle EGD=48^{\circ}\), then \( \angle FGE = 90 - 48=42^{\circ}\).

Step2: Use the straight - angle property

The sum of angles around a straight line is \(180^{\circ}\). So, \( \angle FGE+(3x + 3)^{\circ}=180^{\circ}\). Substitute \( \angle FGE = 42^{\circ}\) into the equation: \(42+(3x + 3)=180\). Simplify the left - hand side: \(3x+(42 + 3)=3x + 45\). So the equation is \(3x + 45=180\).

Step3: Solve the equation for \(x\)

Subtract 45 from both sides of the equation \(3x+45 = 180\):
\(3x+45-45=180 - 45\)
\(3x=135\)
Divide both sides by 3: \(x=\frac{135}{3}=45\)

Answer:

The equation is \(3x + 45 = 180\) and \(x = 45\)