To find the missing bearing, we need to understand that the bearing given is a compass bearing relative to the north. You provided:

• Exterior bearing: $N31^\circ 06' 43" W$
• Interior angle: $116^\circ 41' 36"$

Explanation:

• The bearing is measured clockwise from the north.
• Interior angle refers to the angle between the bearing and a line at that point, usually forming part of a geometric figure (e.g., a triangle).

To find the complementary bearing (or the one that forms part of the exterior):

1. The exterior bearing can be written as $31^\circ 06' 43"$ west of north, which means the complementary bearing, moving clockwise, can be calculated by subtracting it from $360^\circ$.

2. Subtracting the exterior bearing from 360°:

$360^\circ - (31^\circ 06' 43") = 328^\circ 53' 17"$

3. Now, to incorporate the interior angle, the bearing measured clockwise from the north:

$\text{New bearing} = 328^\circ 53' 17" - 116^\circ 41' 36"$

Let's calculate that:

$328^\circ 53' 17" - 116^\circ 41' 36" = 212^\circ 11' 41"$

This gives the final bearing.

Answer:

The missing bearing is $212^\circ 11' 41"$.

Would you like a detailed explanation of how bearings work or additional help? Here are some related questions:

1. How can bearings be used in navigation?
2. How does a bearing differ from an angle in geometry?
3. What are compass quadrants, and how do they relate to bearings?
4. Can you calculate back bearings from given information?
5. How do you convert a bearing from degrees, minutes, and seconds to decimal degrees?

Tip: When dealing with bearings, always remember the convention that bearings are measured clockwise from the north in most navigation scenarios.