Question

in the diagram, lines l, m are parallel, and line k is a transversal. the angles are (3x + 10)° and (4x - 10)°. find the value of x.

Explanation:

Step1: Identify the relationship

Since lines \( l \) and \( m \) are parallel, and \( k \) is a transversal, the angles \( (4x - 10)^\circ \) and \( (3x + 10)^\circ \) are alternate exterior angles, so they are equal.
\[
4x - 10 = 3x + 10
\]

Step2: Solve for \( x \)

Subtract \( 3x \) from both sides:
\[
4x - 3x - 10 = 3x - 3x + 10
\]
\[
x - 10 = 10
\]
Add 10 to both sides:
\[
x - 10 + 10 = 10 + 10
\]
\[
x = 20
\]

Answer:

\( x = 20 \)