Question

solve for x. x = save answer (diagram includes lines with angles ( 81^circ ) and ( (3x + 27)^circ ) formed by parallel lines and a transversal)

Explanation:

Step1: Identify the relationship

Since lines \( NM \) and \( LO \) are parallel (indicated by the red arrows), and \( JK \) is a transversal, the corresponding angles \( (3x + 27)^\circ \) and \( 81^\circ \) are equal. So we set up the equation:
\( 3x + 27 = 81 \)

Step2: Solve for \( x \)

Subtract 27 from both sides:
\( 3x = 81 - 27 \)
\( 3x = 54 \)

Divide both sides by 3:
\( x = \frac{54}{3} \)
\( x = 18 \)

Answer:

\( 18 \)