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 \boxed{}° to resume a due west course.
(type a whole number)

Explanation:

Part a

Step1: Analyze the direction change

When the boat turned \(50^\circ\) north of due west, to get back to due west, the angle to turn back is equal to the angle of the turn from the original direction.

Step2: Determine the angle

The angle she needs to turn the wheel is \(50^\circ\) because the turn from due west to \(50^\circ\) north of west is \(50^\circ\), so to return to due west, she turns back by the same \(50^\circ\).

The angles are alternate interior angles (or related to parallel lines and transversal, here the path before and after the turn are parallel, and the turn angle is the angle between them). The angles (the turn angle and the angle to return) are congruent because they are equal in measure (\(50^\circ\) each), representing the same angle of deviation from the due - west path.

Answer:

\(50\)

Part b