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What is the angular closure of the following 6-sided interior angle traverse?

Angles are in degrees, minutes, and seconds:
- A: 87° 54' 14"
- B: 90° 32' 45"
- C: 102° 43' 31"
- D: 99° 24' 34"
- E: 156° 01' 55"
- F: 183° 23' 07"

Correct to 2 seconds.

Answer :

Final answer:

The angular closure of the given 6-sided interior angle traverse is approximately 0.9984 degrees.

Explanation:

The angular closure of a 6-sided interior angle traverse can be calculated by converting the given angles from degrees, minutes, and seconds to decimal degrees, and then summing them.

Let's convert the given angles to decimal degrees:

  • Angle A: 87.54-14 = 87 degrees + 54 minutes + 14 seconds = 87.9039 degrees
  • Angle B: 90-32-45 = 90 degrees + 32 minutes + 45 seconds = 90.5458 degrees
  • Angle C: 102-43-31 = 102 degrees + 43 minutes + 31 seconds = 102.7253 degrees
  • Angle D: 99-24-34 = 99 degrees + 24 minutes + 34 seconds = 99.4094 degrees
  • Angle E: 156-01-55 = 156 degrees + 1 minute + 55 seconds = 156.0319 degrees
  • Angle F: 183-23-07 = 183 degrees + 23 minutes + 7 seconds = 183.3853 degrees

Now, let's calculate the sum of the converted angles:

Sum = 87.9039 + 90.5458 + 102.7253 + 99.4094 + 156.0319 + 183.3853 = 719.0016 degrees

The expected sum for a closed 6-sided polygon is (6-2) * 180 = 720 degrees.

Therefore, the angular closure of the given 6-sided interior angle traverse is:

Angular Closure = Expected Sum - Sum = 720 - 719.0016 = 0.9984 degrees

Learn more about angular closure of 6-sided interior angle traverse here:

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