Question

1. this map shows that the airports in tallahassee (tlh) and orlando (mco) lie on parallel latitude lines. the flight path from tallahassee to orlando forms a 37° angle with the latitude line through tallahassee.

if the same flight path is used for the return trip, which angle will be formed by the flight path and the latitude line through orlando?
a 37°
b. 53°
c. 127°
d. 143°

Explanation:

Step1: Identify Parallel Lines and Transversal

The latitude lines are parallel, and the flight path is a transversal. So, we can use properties of parallel lines (alternate interior angles, consecutive interior angles, etc.). The angle at TLH is \(37^\circ\) with its latitude line. The return trip's angle with MCO's latitude line: since the latitude lines are parallel, the angle between the flight path and MCO's latitude line and the angle at TLH are related to supplementary or complementary? Wait, no—actually, the two latitude lines are parallel, and the flight path is a transversal. The angle at TLH is \(37^\circ\), and we need the angle at MCO. Wait, the sum of the angle at TLH and the angle at MCO should be \(90^\circ\)? No, wait, let's think about consecutive interior angles or alternate angles. Wait, the angle between the flight path and TLH's latitude is \(37^\circ\), so the angle between the flight path and the vertical (if we consider north-south) would be \(90 - 37 = 53^\circ\)? No, wait, no. Wait, the latitude lines are horizontal (parallel), and the flight path is a transversal. The angle at TLH is \(37^\circ\) (between flight path and TLH's latitude). Then, the angle at MCO (between flight path and MCO's latitude) should be \(90 - 37 = 53^\circ\)? Wait, no, wait. Wait, the two latitude lines are parallel, so the alternate interior angles? Wait, no, the flight path is a straight line. So, the angle at TLH is \(37^\circ\) (with the horizontal), so the angle at MCO (with the horizontal) should be \(90 - 37 = 53^\circ\)? Wait, let's check: the sum of \(37^\circ\) and the angle we need should be \(90^\circ\) if they are complementary? Wait, no, actually, the angle between the flight path and the latitude line (horizontal) at TLH is \(37^\circ\), so the angle between the flight path and the vertical is \(90 - 37 = 53^\circ\), but when we go to MCO, the latitude line is horizontal, so the angle between the flight path and MCO's latitude line would be \(90 - 37 = 53^\circ\)? Wait, no, maybe I'm overcomplicating. Wait, the two latitude lines are parallel, so the consecutive interior angles are supplementary? Wait, no, the flight path is a transversal. The angle at TLH is \(37^\circ\), so the angle at MCO (between flight path and MCO's latitude) should be \(180 - 37 - 90 = 53^\circ\)? Wait, no, let's use the fact that the sum of the angle at TLH (\(37^\circ\)) and the angle at MCO is \(90^\circ\)? Wait, no, let's calculate: if the angle between the flight path and TLH's latitude is \(37^\circ\), then the angle between the flight path and the north direction (vertical) is \(90 - 37 = 53^\circ\). Then, at MCO, the angle between the flight path and MCO's latitude (horizontal) would be \(53^\circ\)? Wait, no, maybe I made a mistake. Wait, the answer options are \(37^\circ\), \(53^\circ\), \(127^\circ\), \(143^\circ\). So, \(37 + 53 = 90\), \(37 + 127 = 164\), \(37 + 143 = 180\). Wait, the angle at TLH is \(37^\circ\), so the angle at MCO should be \(180 - 37 - 90 = 53^\circ\)? Wait, no, let's think of the two latitude lines as parallel, so the alternate interior angles: no, the angle at TLH is \(37^\circ\) (between flight path and TLH's latitude), so the angle between flight path and MCO's latitude is \(180 - 37 - 90 = 53^\circ\)? Wait, maybe the correct approach is: the angle between the flight path and TLH's latitude is \(37^\circ\), so the angle between the flight path and the perpendicular to the latitude (north-south) is \(90 - 37 = 53^\circ\). Then, at MCO, the angle between the flight path and MCO's latitude (which is parallel to TLH's latitude) would be \(53^\circ\), because the north-south line is perpendicular to both latitude lines. So, the angle at MCO is \(53^\circ\), which is option B.

Wait, let's verify: if the latitude lines are parallel (horizontal), and the flight path is a transversal. The angle at TLH is \(37^\circ\) (between flight path and TLH's latitude). Then, the angle between the flight path and the vertical (north-south) is \(90 - 37 = 53^\circ\). Since the latitude lines are horizontal, the angle between the flight path and MCO's latitude (horizontal) is equal to the angle between the flight path and the vertical, which is \(53^\circ\). So the answer is \(53^\circ\), option B.

Step2: Calculate the Angle

Wait, another way: the sum of the angle at TLH (\(37^\circ\)) and the angle at MCO should be \(90^\circ\)? No, \(37 + 53 = 90\), so that makes sense. Because the flight path is a straight line, and the two latitude lines are parallel, so the angles with the latitude lines are complementary? Wait, maybe. So \(90 - 37 = 53^\circ\), so the angle at MCO is \(53^\circ\), which is option B.

Answer:

B. \(53^\circ\)