Question

find the value of x for which l is parallel to m. the diagram is not to scale. 80° (3x - 43)° 123 41 80 100

Explanation:

Step1: Identify angle - relationship

When two lines are parallel, alternate - interior angles are equal. Here, the angle of measure $(3x - 43)^{\circ}$ and the $80^{\circ}$ angle are alternate - interior angles. So, we set up the equation $3x-43 = 80$.

Step2: Solve the equation for x

Add 43 to both sides of the equation: $3x-43 + 43=80 + 43$, which simplifies to $3x=123$.

Step3: Isolate x

Divide both sides of the equation $3x = 123$ by 3: $\frac{3x}{3}=\frac{123}{3}$, so $x = 41$.

Answer:

B. 41