Question

11.
there is a diagram with three lines: line k (a transversal) intersecting two parallel lines l and m. the angle formed between line k and line l is ((7x + 5)^circ), and the angle formed between line k and line m (on the opposite side relative to the angle with line l) is ((5x + 19)^circ).

Explanation:

Step1: Identify the relationship

Since lines \( \ell \) and \( m \) are parallel, and \( k \) is a transversal, the alternate - interior angles are equal. So we can set up the equation \( 7x + 5=5x + 19 \).

Step2: Solve for \( x \)

Subtract \( 5x \) from both sides of the equation:
\( 7x+5 - 5x=5x + 19-5x \)
\( 2x+5 = 19 \)

Then subtract 5 from both sides:
\( 2x+5 - 5=19 - 5 \)
\( 2x=14 \)

Divide both sides by 2:
\( x=\frac{14}{2}=7 \)

Answer:

\( x = 7 \)