Question

what must be the value of x so that lines c and d are parallel lines cut by transversal p? 12 18 81 99

Explanation:

Step1: Identify angle relationship

Since lines \( c \) and \( d \) are parallel and cut by transversal \( p \), the angles \( (3x + 45)^\circ \) and \( 81^\circ \) are same - side interior angles, which are supplementary. So, \( (3x + 45)+81 = 180 \).

Step2: Simplify the equation

First, combine like terms: \( 3x+45 + 81=3x + 126 \). So the equation becomes \( 3x+126 = 180 \).

Step3: Solve for \( x \)

Subtract 126 from both sides: \( 3x=180 - 126 \), which simplifies to \( 3x = 54 \). Then divide both sides by 3: \( x=\frac{54}{3}=18 \).

Answer:

18