Question

given mue of x. (2x-29)° (7x+2)° answer attempt 1 out of 2 x = submit answer

Explanation:

Step1: Identify the relationship (alternate interior angles)

Since \( m \parallel n \) and \( t \) is a transversal, the angles \( (2x - 29)^\circ \) and \( (7x + 2)^\circ \) are alternate interior angles. Alternate interior angles are equal when lines are parallel. So we set up the equation:
\( 2x - 29 = 7x + 2 \)

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides:
\( -29 = 5x + 2 \)
Subtract 2 from both sides:
\( -31 = 5x \)
Divide both sides by 5: Wait, no, wait. Wait, maybe I made a mistake. Wait, alternate interior angles? Wait, no, maybe they are same - side interior angles? Wait, no, looking at the diagram, if \( m \parallel n \), and the angles are on the same side? Wait, no, maybe I mixed up. Wait, actually, if \( m \parallel n \), and the two angles are same - side interior angles, they should be supplementary. Wait, maybe the initial assumption was wrong. Let's re - examine.

Wait, the correct relationship: when two parallel lines are cut by a transversal, same - side interior angles are supplementary (sum to \( 180^\circ \)). Let's check the positions. The angle \( (2x - 29)^\circ \) and \( (7x + 2)^\circ \) are same - side interior angles. So the correct equation is \( (2x - 29)+(7x + 2)=180 \)

Step3: Combine like terms

\( 2x+7x-29 + 2=180 \)
\( 9x-27 = 180 \)

Step4: Solve for \( x \)

Add 27 to both sides:
\( 9x=180 + 27 \)
\( 9x=207 \)
Divide both sides by 9:
\( x=\frac{207}{9}=23 \)

Answer:

\( x = 23 \)