Traverse geometry — if the whole-circle bearings of lines AB and BC are 146° 30′ and 68° 30′ respectively, compute the included interior angle ABC.

Introduction / Context:
Included angles in traverses are often derived from line bearings. Converting between forward and back bearings and then taking appropriate differences ensures consistency in traverse adjustment and plotting. This problem reinforces the method for computing an interior angle at a station using whole-circle bearings (WCBs).

Given Data / Assumptions:

• Bearing of AB (WCB) = 146° 30′.
• Bearing of BC (WCB) = 68° 30′.
• Included angle ABC is the angle from BA to BC, measured inside the traverse at station B.

Concept / Approach:

First find the back bearing of AB to get the direction of BA at station B. Back bearing = forward bearing ± 180°. Then, the interior angle at B is the clockwise (or suitable) angle from BA to BC, accounting for 0–360° wrap-around. The smaller of the two possible angles consistent with the traverse direction is taken as the interior angle when the traverse proceeds A→B→C.

Step-by-Step Solution:

Verification / Alternative check:

Graphical sketching with a protractor or computing the smaller angular difference between directions confirms 102° as the interior angle at B.

Why Other Options Are Wrong:

78° or 45° — arise from incorrect difference order or omission of wrap-around at 360°.
None of these — incorrect because 102° is correct.

Common Pitfalls:

Forgetting to convert to the back bearing at B; subtracting in the wrong order; ignoring the 0–360° wrap when crossing north.

Final Answer:

102°