Question

find the value of x in the diagram below. please select the best answer from the choices provided

Explanation:

Step1: Use the property of consecutive interior angles

In a trapezoid (the given figure is a trapezoid as it has one pair of parallel sides), consecutive interior angles are supplementary. So, \((x + 40)+x=180\).

Step2: Simplify the equation

Combine like - terms: \(x + 40+x=180\) becomes \(2x+40 = 180\).
Subtract 40 from both sides: \(2x=180 - 40\), so \(2x=140\).

Step3: Solve for \(x\)

Divide both sides by 2: \(x=\frac{140}{2}\).

Answer:

\(x = 70\), so the answer is C.