Question

lines b and c are parallel.
what is the measure of ∠6?
(13x + 9)° (5x + 9)°
m∠6 = 126° m∠6 = 117°
m∠6 = 54° m∠6 = 45°

Explanation:

Step1: Identify corresponding angles

Since b || c, (5x+9)° and (13x+9)° are supplementary (consecutive interior angles).
Equation: $5x + 9 + 13x + 9 = 180$

Step2: Solve for x

Combine terms: $18x + 18 = 180$
Subtract 18: $18x = 162$
Divide by 18: $x = 9$

Step3: Find m∠6

∠6 = (5x+9)° (vertical angles).
Substitute x=9: $5(9)+9 = 54$

Answer:

The option with m∠6=54° (identifier depends on original labeling, e.g., if it's the bottom-right option: "m∠6=54°")