What is the angular misclosure for a five-sided polygon traverse with observed exterior angles of 252° 26’ 39”, 255° 55’ 15”, 277° 15’ 55”, 266° 35’ 03”, and 207° 47’ 07”?

Question

What is the angular misclosure for a five-sided polygon traverse with observed exterior angles of 252°

26’ 39”, 255° 55’ 15”, 277° 15’ 55”, 266° 35’ 03”, and 207° 47’ 07”?

Answer 1

To find the angular misclosure for a polygon traverse, we need to calculate the sum of the observed exterior angles and compare it to the expected sum for a closed polygon.

Given the observed exterior angles:

252° 26’ 39”

255° 55’ 15”

277° 15’ 55”

266° 35’ 03”

207° 47’ 07”

First, we need to convert the angles from degrees, minutes, and seconds to decimal degrees for ease of calculation.

252° 26’ 39” = 252 + 26/60 + 39/3600 = 252.444167°

255° 55’ 15” = 255 + 55/60 + 15/3600 = 255.920833°

277° 15’ 55” = 277 + 15/60 + 55/3600 = 277.265278°

266° 35’ 03” = 266 + 35/60 + 3/3600 = 266.584167°

207° 47’ 07” = 207 + 47/60 + 7/3600 = 207.785278°

Next, we calculate the sum of the observed exterior angles:

Sum = 252.444167 + 255.920833 + 277.265278 + 266.584167 + 207.785278 = 1259.999723°

For a closed polygon, the sum of the exterior angles should be (n-2) * 180°, where n is the number of sides of the polygon.

For a five-sided polygon, the expected sum of the exterior angles is (5-2) * 180° = 540°.

Now we can calculate the angular misclosure:

Angular Misclosure = Sum of observed exterior angles - Expected sum

Angular Misclosure = 1259.999723° - 540°

Angular Misclosure = 719.999723°

Therefore, the angular misclosure for the five-sided polygon traverse is approximately 719.999723°.