Given that lines $b$ and $c$ are parallel and angle $6$ is formed by a transversal intersecting these lines, what is the measure of angle $6$?

• A. $m6=45°$
• B. $m6=117°$
• C. $m6=54°$
• D. $m6=126°$

Answer: (B)

Verified step by step guidance

1. Identify the relationship between the given angle 6 and the other angles formed by the transversal intersecting the parallel lines b and c. Since lines b and c are parallel, corresponding angles, alternate interior angles, or consecutive interior angles can be used to find the measure of angle 6.
2. Recall that when a transversal crosses two parallel lines, alternate interior angles are congruent, and consecutive interior angles are supplementary (sum to 180°). Determine which of these relationships applies to angle 6 based on its position relative to the transversal and the parallel lines.
3. Use the given angle measure (for example, if angle 6 is supplementary to a known angle, set up the equation: \(m\angle 6 + m\angle x = 180^\circ\), where \(m\angle x\) is the known angle measure). If angle 6 corresponds to an alternate interior angle, then \(m\angle 6 = m\angle x\).
4. Solve the equation for \(m\angle 6\) by substituting the known angle value and performing the necessary arithmetic operations to isolate \(m\angle 6\).
5. Verify the result by checking if the found measure of angle 6 satisfies the properties of angles formed by a transversal intersecting parallel lines, ensuring consistency with the given information.