A traverse with five sides has interior angles with the following measures: 121deg 45 min: 118 deg 25 min; 87 deg 32 min; 98deg 34min, and 113 deg 54 min. Does the traverse close? If not, determne the error in the traverse.
We must be looking at some kind of polygon of 5 sides.
If closed, the sum of the interior angles would be
180(5-2) = 540°
I added them up and got 540° 10'
So the "traverse" is not possible
To determine if the traverse is closed or if there is an error, we need to calculate the sum of the interior angles.
First, convert the minutes to degrees by dividing by 60.
121 degrees 45 minutes = 121 + (45/60) = 121.75 degrees
118 degrees 25 minutes = 118 + (25/60) = 118.4167 degrees
87 degrees 32 minutes = 87 + (32/60) = 87.5333 degrees
98 degrees 34 minutes = 98 + (34/60) = 98.5667 degrees
113 degrees 54 minutes = 113 + (54/60) = 113.9 degrees
Now, add up all these angles:
121.75 + 118.4167 + 87.5333 + 98.5667 + 113.9 = 539.1667 degrees
Since a traverse with five sides should have a total of 540 degrees (540 degrees is the sum of all angles in a closed traverse), there is a discrepancy of 0.8333 degrees (540 - 539.1667).
Therefore, the traverse does not close, and the error in the traverse is 0.8333 degrees.