Question

the figure shows two lines cut by a transversal.
what value of b shows that the lines are parallel?
use the number pad to enter your answer in the box.
$b = square$

Explanation:

Step1: Use the property of parallel lines

When two parallel lines are cut by a transversal, the corresponding angles are equal. Here, \((5b + 16)^{\circ}\) and \((b+32)^{\circ}\) are supplementary (they form a linear - pair if the lines are parallel). So, \(5b + 16+b + 32=180\).

Step2: Simplify the equation

Combine like terms: \(6b+48 = 180\).

Step3: Solve for \(b\)

Subtract 48 from both sides: \(6b=180 - 48\), so \(6b = 132\). Then divide both sides by 6: \(b=\frac{132}{6}\).

Answer:

\(22\)