Questions: Look at the diagram. Which equation can be used to solve for x ? 6x-6=180 6x-6=90 12x=90 12x=180 Solve for x. x=

Transcript text: Look at the diagram. Which equation can be used to solve for $x$ ? $6 x-6=180$ $6 x-6=90$ $12 x=90$ $12 x=180$ Solve for $x$. \[ x= \] $\square$

Solution

Solution Steps

Step 1: Find the relationship between the angles

Angles FCD and ECG are vertical angles, and vertical angles are congruent. Therefore, the measure of angle FCD is equal to the measure of angle ECG.

Step 2: Set up an equation

Angle FCD is given as (4x - 6)° and angle ECG is given as (2x)°. We can set up the equation 4x - 6 = 2x.

Step 3: Simplify the equation

Adding 6 to both sides gives 4x = 2x + 6. Subtracting 2x from both sides gives 2x = 6.

Step 4: Solve for x

Dividing both sides by 2 gives x = 3.

Final Answer: The correct equation is 4x - 6 = 2x and x = 3

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