Question

1. given the parallel lines cut by a transversal, find the value of ( x ):

a. 35
b. 12
c. 17
d. 64

Explanation:

Step1: Use property of parallel lines

When parallel lines are cut by a transversal, consecutive interior angles are supplementary. So \(107+(3x + 2)=180\).

Step2: Simplify the equation

\(3x+109 = 180\) (combine like - terms \(107 + 2\)).

Step3: Solve for \(x\)

Subtract \(109\) from both sides: \(3x=180 - 109\), so \(3x = 71\). Then \(x=\frac{71}{3}\) (This is wrong. Wait, no! Wait, actually, when two parallel lines are cut by a transversal, the angles \(107^{\circ}\) and \((3x + 2)^{\circ}\) are congruent as they are alternate exterior angles. So \(3x+2=107\)).

Step3 (corrected): Solve the correct equation

\(3x+2 = 107\). Subtract \(2\) from both sides: \(3x=107 - 2=105\). Then divide both sides by \(3\): \(x=\frac{105}{3}=35\).

Answer:

A. 35