In the figure shown, line AB is parallel to line CD.
Part A: What is the measure of angle x? Show your work. (5 points)
Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal. (5 points)
AB and CD are parallel lines, and PQ and PR are transversals which intersect AB at P and CD at Q and R. Angle APQ is labeled as 62 degrees, angle QPR is equal to x, angle PRD is equal to 115 degrees.
To find the measure of angle x, we can use the fact that when a transversal intersects two parallel lines, alternate interior angles are congruent.
Part A: To find angle x, we need to identify the alternate interior angles with x. In this case, angle QPR and angle APQ are alternate interior angles. Since angle APQ is given as 62 degrees, we can conclude that angle QPR is also 62 degrees. Therefore, the measure of angle x is 62 degrees.
Part B: We found the measure of angle x by using the alternate interior angles relationship. When a transversal intersects two parallel lines, alternate interior angles are congruent. In this case, angle QPR and angle APQ are alternate interior angles. Since angle APQ is 62 degrees, we can conclude that angle QPR is also 62 degrees. Therefore, the measure of angle x is 62 degrees.