Question

solve for x. diagram: horizontal line ab (arrows a→, b←), intersecting two parallel vertical lines cd (arrows c↑, d↓) and ef (arrows e↑, f↓) at points g and h, respectively. angle at g: (3x + 24)°, angle at h: (5x - 12)°. \save answer\ button and x = blank box.

Explanation:

Step1: Identify alternate interior angles

Since lines \( CD \) and \( EF \) are parallel (marked by red arrows) and \( AB \) is a transversal, \( \angle CGH \) and \( \angle EHG \) are alternate interior angles, so they are equal. Thus, \( 3x + 24 = 5x - 12 \).

Step2: Solve for \( x \)

Subtract \( 3x \) from both sides: \( 24 = 2x - 12 \).
Add 12 to both sides: \( 36 = 2x \).
Divide by 2: \( x = 18 \).

Answer:

\( 18 \)