Given that lines b and c are parallel and angle 2 is formed by a transversal intersecting these lines, if $m\angle 2=50°$, what is the measure of angle 2?

• A. $m\angle 2=120°$
• B. $m\angle 2=50°$
• C. $m\angle 2=130°$
• D. $m\angle 2=31°$

Answer: (B)

Verified step by step guidance

1. Identify the given information: lines b and c are parallel, and angle 2 is formed by a transversal intersecting these lines. The measure of angle 2 is given as 50°.
2. Recall that when a transversal intersects two parallel lines, corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary (sum to 180°).
3. Since angle 2 is given as 50°, and it is formed by the transversal with the parallel lines, determine which angle relationship applies (e.g., corresponding, alternate interior, or consecutive interior) to find the measure of the angle in question.
4. Use the appropriate angle relationship formula. For example, if angle 2 corresponds to another angle on the parallel lines, then their measures are equal: \(m\angle 2 = 50^\circ\).
5. Conclude that the measure of angle 2 is 50°, based on the properties of parallel lines and the transversal.