Final answer:
In a closed traverse survey of a 7-sided parcel where deflection angles are measured instead of interior angles, the total sum of all 7 deflection angles should be 360 degrees.
Step-by-step explanation:
In a closed traverse survey of a 7-sided parcel where deflection angles are measured instead of interior angles, the total sum of all 7 deflection angles should be 360 degrees.
To understand why this is the case, we can consider that in a closed polygon, the sum of all interior angles is always equal to (n-2) * 180 degrees, where n is the number of sides of the polygon. In this case, since the parcel has 7 sides, the sum of all interior angles would be (7-2) * 180 = 900 degrees.
However, since deflection angles are measured instead of interior angles, we need to consider that these angles are measured with respect to a reference, usually the previous line segment. So, in a closed traverse where deflection angles are used, the sum of all deflection angles should be equal to the sum of all interior angles plus a correction angle, which will make the total sum of all 7 deflection angles equal to 360 degrees.
For example, if we assume that the correction angle for this particular survey is 540 degrees, then the sum of all 7 deflection angles would be 900 + 540 = 1440 degrees. However, since the total sum of all angles in a closed polygon should always be 360 degrees, we can subtract the correction angle from the sum of all interior angles to find the correct total sum of all deflection angles, which is 1440 - 1080 = 360 degrees.