Question

1. (5x + 3)° and (9x - 33)° with parallel lines ( l ) (top) and ( m ) (bottom) cut by a transversal (diagram shows the two horizontal parallel lines and the transversal forming the angles)

Explanation:

Step1: Identify the relationship

Since lines \( l \) and \( m \) are parallel, the two angles \( (5x + 3)^\circ \) and \( (9x - 33)^\circ \) are alternate interior angles, so they are equal.
\[ 5x + 3 = 9x - 33 \]

Step2: Solve for \( x \)

Subtract \( 5x \) from both sides:
\[ 3 = 4x - 33 \]
Add 33 to both sides:
\[ 36 = 4x \]
Divide both sides by 4:
\[ x = 9 \]

Step3: Find the angle measure (optional, if needed)

Substitute \( x = 9 \) into \( 5x + 3 \):
\[ 5(9) + 3 = 45 + 3 = 48^\circ \]
Or into \( 9x - 33 \):
\[ 9(9) - 33 = 81 - 33 = 48^\circ \]

Answer:

\( x = 9 \) (and the angle measure is \( 48^\circ \) if needed)