Question

solve for x.

x =

Explanation:

Step1: Use the property of corresponding angles

Since \(CD\parallel EF\), the angle \((3x - 10)^{\circ}\) and the angle adjacent to \(110^{\circ}\) (which is \(180^{\circ}- 110^{\circ}=70^{\circ}\)) are corresponding angles. So, \(3x-10 = 70\).

Step2: Solve the equation for \(x\)

Add \(10\) to both sides of the equation \(3x-10 = 70\):
\(3x-10 + 10=70 + 10\), which simplifies to \(3x=80\).
Then divide both sides by \(3\): \(x=\frac{80}{3}\approx26.67\). Wait, no, wait! Wait, actually, the angle \((3x - 10)\) and \(110^{\circ}\) are same - side interior angles. So \(3x-10+110 = 180\) (because same - side interior angles are supplementary when two parallel lines are cut by a transversal).

Step3: Solve the correct equation

Simplify \(3x-10 + 110=180\) to \(3x+100 = 180\).
Subtract \(100\) from both sides: \(3x+100-100 = 180-100\), so \(3x=80\).
Divide both sides by \(3\): \(x = 40\).

Answer:

\(40\)