Rectangle bearings and parallel sides: ABCD is a rectangular plot. If the whole-circle bearing (WCB) of side AB is 75°, what is the bearing of the opposite side DC (taken from D to C)?

Introduction / Context:
In plane surveying, parallel lines have identical bearings when measured in the same direction. A rectangle has opposite sides parallel, so the bearing of DC should match AB provided we observe DC from D to C (i.e., the same direction of travel along that pair of parallels). This conceptual check is common in traverse adjustment and plotting.

Given Data / Assumptions:

• ABCD is a rectangle, so AB ∥ DC and BC ∥ AD.
• Bearing of AB (A→B) is 75° (WCB).
• We need bearing of DC from D→C.

Concept / Approach:
Parallel lines share the same direction. The side DC when taken from D→C runs parallel and in the same sense as AB from A→B. Therefore, their bearings are equal. Note the difference between a “forward bearing” of a line and its “back bearing” (which differs by 180°). Here we are not asked for the back bearing of AB; we are asked for the forward bearing of DC, which equals the forward bearing of AB.

Step-by-Step Solution:

Verification / Alternative check:
Back bearing of AB would be 75° + 180° = 255°. That would correspond to C→D, not D→C. This cross-check confirms that D→C must be 75° to stay parallel to A→B in the same sense.

Why Other Options Are Wrong:

• 255°: this is the back bearing of AB (B→A) or the bearing of CD (C→D), not of DC.
• 105° and 285°: do not match either the parallel or perpendicular directions in this case.

Common Pitfalls:
Confusing which way along a side the bearing is taken; mixing forward and back bearings; forgetting that opposite sides of a rectangle are parallel and have identical forward bearings when taken in consistent directions.

Final Answer:
75°