Question

the image shows parallel lines cut by a transversal. the expressions represent unknown angle measurements. what is the value of x? a 7 b 10 c 13 d 16

Explanation:

Step1: Use the property of same - side interior angles

When two parallel lines are cut by a transversal, same - side interior angles are supplementary. So, \((x + 55)+(x + 93)=180\).

Step2: Simplify the equation

Combine like terms: \(x+x+55 + 93=180\), which is \(2x+148 = 180\).

Step3: Solve for \(x\)

Subtract 148 from both sides: \(2x=180 - 148\), so \(2x=32\). Then divide both sides by 2: \(x=\frac{32}{2}=16\).

Answer:

D. 16