Question

lines, angles, and polygons finding angle measures given two parallel lines cut by a transversal two parallel lines are cut by a transversal as shown below. suppose (mangle6 = 103^{circ}). find (mangle1) and (mangle3).

Explanation:

Step1: Identify angle - relationship for ∠1 and ∠6

∠1 and ∠6 are alternate exterior angles. When two parallel lines are cut by a transversal, alternate exterior angles are congruent.
So, \(m\angle1=m\angle6\)

Step2: Identify angle - relationship for ∠3 and ∠6

∠3 and ∠6 are same - side interior angles. When two parallel lines are cut by a transversal, same - side interior angles are supplementary, that is \(m\angle3 + m\angle6=180^{\circ}\). So, \(m\angle3=180^{\circ}-m\angle6\)

Answer:

\(m\angle1 = 103^{\circ}\)
\(m\angle3 = 77^{\circ}\)