In the figure, a∥e , m∥n , and m∠2 = 117°. What is m∠5 ? 63° 90° 117° 180°

To determine the measure of angle 5 (m∠5), we will need to use the given information that line a is parallel to line e, and line m is parallel to line n. Since you've indicated that m∠2 = 117°, we can find the measure of m∠5 by identifying the relationship between these angles.

Given that lines a and e are parallel, if angle 2 is a corresponding angle to any angle formed by line e and a transversal, then that angle would also be 117°. However, without a diagram, we cannot definitively determine which angle corresponds with angle 2.

If angle 5 is on the same side of the transversal as angle 2 and within the parallel lines a and e (or m and n), angle 2 and angle 5 could be same-side interior angles. Same-side interior angles are supplementary, which means their measures add up to 180°. If that's the case:

m∠5 = 180° - m∠2 m∠5 = 180° - 117° m∠5 = 63°

If angle 5 is not an interior angle but is indeed a corresponding angle or an alternate exterior angle to angle 2, then it would also measure 117°.

Since the information provided is not enough to determine the exact position of angle 5 with respect to angle 2 with certainty, we can only speculate based on typical relationships between angles. With the information given, m∠5 could be either 63° or 117°. But since we are told that lines m and n are parallel, if angle 5 corresponds with angle 2 across the two lines and the transversal, then m∠5 would be 117°.