Question

margaret is in a boat traveling due west. she turned the boat 50° north of due west for a couple of minutes to get around a peninsula. then she resumed due west again
a. how many degrees would she turn the wheel to resume a due west course?
b. what type of angles did she use? are the angles congruent or supplementary?

a. margaret turned the wheel 50° to resume a due west course.
(type a whole number)
b. margaret used alternate interior angles, which are congruent, to resume her course.

Explanation:

Part (a)

Step1: Analyze the path

The boat was moving west, turned \(50^\circ\) north of west, then to resume west, the turn angle should be equal to the angle of deviation (since the original and final paths are parallel, the alternate interior angles are equal).

Step2: Determine the turn angle

The deviation angle was \(50^\circ\), so the turn angle to resume west is \(50^\circ\).

• The angles formed by the parallel west paths and the transversal (the boat's turning path) are alternate interior angles. By the alternate interior angles theorem, these angles are congruent (equal in measure).

Answer:

\(50\)

Part (b)