Question

in the figure shown below, line m and line n are parallel. what is the value of x?
diagram: two parallel lines (m, n) cut by a transversal, forming angles ( 3x - 10 ) (on line m) and ( 5x + 30 ) (on line n).
( x = ) input box with calculator icon

Explanation:

Step1: Identify angle relationship

Since lines \( m \) and \( n \) are parallel, the angles \( 3x - 10 \) and \( 5x + 30 \) are same - side interior angles, and same - side interior angles are supplementary (their sum is \( 180^{\circ} \)). So we can write the equation:
\( (3x - 10)+(5x + 30)=180 \)

Step2: Simplify the left - hand side of the equation

Combine like terms: \( 3x+5x-10 + 30=180 \)
\( 8x + 20=180 \)

Step3: Solve for \( x \)

Subtract 20 from both sides of the equation:
\( 8x+20 - 20=180 - 20 \)
\( 8x=160 \)
Divide both sides by 8:
\( x=\frac{160}{8}=20 \)

Answer:

\( 20 \)