Question

in the figure shown, lines m and n are parallel, and line t intersects both lines, a = 47, find the values of b and c.

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. Since \(a\) and \(b\) are vertical angles, \(b=a\).
\(b = 47\)

Step2: Identify corresponding - angle relationship

Corresponding angles formed by a transversal intersecting two parallel lines are equal. Since \(a\) and \(c\) are corresponding angles and \(m\parallel n\), \(c=a\).
\(c = 47\)

Answer:

\(b = 47\), \(c = 47\)