Question

d the value of x.

Explanation:

Step1: Identify angle relationship

Since lines \( m \) and \( n \) are parallel, and transversal \( t \) intersects them, the angles \( (9x + 4)^\circ \) and \( (2x - 11)^\circ \) are same - side interior angles (or supplementary angles, as they should add up to \( 180^\circ \) because of the parallel lines and transversal). So we set up the equation:
\( (9x + 4)+(2x - 11)=180 \)

Step2: Simplify the left - hand side

Combine like terms: \( 9x+2x + 4-11 = 180 \), which simplifies to \( 11x-7 = 180 \)

Step3: Solve for \( x \)

Add 7 to both sides of the equation: \( 11x-7 + 7=180 + 7 \), so \( 11x=187 \)
Then divide both sides by 11: \( x=\frac{187}{11}=17 \)

Answer:

\( x = 17 \)