Question

14.
(5x + 7)° (8x - 71)°
l m
16.
102° (2x + 12)°

Explanation:

Problem 14 (Assuming we solve this first, dealing with parallel lines and alternate interior angles)

Step1: Identify Angle Relationship

Lines \( l \) and \( m \) are parallel, and the transversal creates alternate interior angles. So \( 5x + 7 = 8x - 71 \).

Step2: Solve for \( x \)

Subtract \( 5x \) from both sides: \( 7 = 3x - 71 \).
Add 71 to both sides: \( 78 = 3x \).
Divide by 3: \( x = 26 \).

Problem 16

Step1: Identify Angle Relationship

The angle \( 102^\circ \) and \( (2x + 12)^\circ \) are same - side interior angles (or supplementary if lines are parallel, assuming parallel lines here). So \( 102+(2x + 12)=180 \).

Step2: Solve for \( x \)

Simplify left - hand side: \( 2x+114 = 180 \).
Subtract 114 from both sides: \( 2x=66 \).
Divide by 2: \( x = 33 \).

Answer:

(for Problem 14): \( x = 26 \)