Question

example 2
find the value of x so that ℓ || m.
7.
image of two parallel lines ℓ and m cut by a transversal k, creating an angle of (2x + 6)° on line ℓ and 130° on line m

Explanation:

Step1: Identify the angle relationship

Since \( \ell \parallel m \) and \( k \) is a transversal, the angles \( (2x + 6)^\circ \) and \( 130^\circ \) are same - side interior angles. Same - side interior angles are supplementary, meaning their sum is \( 180^\circ \). So we can set up the equation:
\( (2x + 6)+130 = 180 \)

Step2: Solve the equation for x

First, simplify the left - hand side of the equation:
\( 2x+6 + 130=2x + 136 \)
So our equation becomes \( 2x+136 = 180 \)
Subtract 136 from both sides of the equation:
\( 2x=180 - 136 \)
\( 2x = 44 \)
Divide both sides by 2:
\( x=\frac{44}{2}=22 \)

Answer:

\( x = 22 \)