how to find angles of quadrilateral survey

[John_Kanute]

Is there enough data per attached land survey to calculate the angles? If so, please let me know the steps to solve.

Thanks

 

[wjm11]

Is there enough data per attached land survey to calculate the angles? If so, please let me know the steps to solve.

Thanks

Yes, all the info is there in the form of bearing angles (all angles measured starting with North as zero and increasing in a clockwise direction). It is hard to read the bearing angles off of your figure however. But for example, the angle of the two lines radiating from the circle labeled "DAK VALLEY ROAD" would be found by subtracting the angle that points almost due North from the angle that points NE: ( 50 degrees, 10 minutes, 42 seconds) minus (whatever those unreadable numbers are). The angle at "IRON FOUND" would be 180 degrees - ( (50 degrees, 10 minutes, 42 seconds) - (0 degrees, 28 minutes(?), 35 seconds(?)). You can check your answers by laying a protractor on the drawing and seeing if your answers approximately match the protractor readings. The sum of all four interior angles must equal 360 degrees.

 

[John_Kanute]

Yes, all the info is there in the form of bearing angles (all angles measured starting with North as zero and increasing in a clockwise direction). It is hard to read the bearing angles off of your figure however. But for example, the angle of the two lines radiating from the circle labeled "DAK VALLEY ROAD" would be found by subtracting the angle that points almost due North from the angle that points NE: ( 50 degrees, 10 minutes, 42 seconds) minus (whatever those unreadable numbers are). The angle at "IRON FOUND" would be 180 degrees - ( (50 degrees, 10 minutes, 42 seconds) - (0 degrees, 28 minutes(?), 35 seconds(?)). You can check your answers by laying a protractor on the drawing and seeing if your answers approximately match the protractor readings. The sum of all four interior angles must equal 360 degrees.

Hello @wjm11, thank you for the help. The bearings are as follows:

1) starting from the cul de sac ( R=65) and starting from the right side and working ccw:
1st leg= N 50'10'42" E ( 407.56 ft )

2nd leg( has two bearings 1 @ N 01'23'27" E ( 45 ft ) & 1 @ N 01'28'55" E ( 384.44 ft )

3rd leg = S 52'10'59" W ( 500.35 ft )

4th leg down to cul de sac = S 03'27'19" E

NOTE: distance from left side to right side of cul de sac = 53.96 ft

Which ones do I subtract to find angles?

 

[wjm11]

Hello @wjm11, thank you for the help. The bearings are as follows:

1) starting from the cul de sac ( R=65) and starting from the right side and working ccw:
1st leg= N 50'10'42" E ( 407.56 ft )

2nd leg( has two bearings 1 @ N 01'23'27" E ( 45 ft ) & 1 @ N 01'28'55" E ( 384.44 ft )

3rd leg = S 52'10'59" W ( 500.35 ft )

4th leg down to cul de sac = S 03'27'19" E

NOTE: distance from left side to right side of cul de sac = 53.96 ft

Which ones do I subtract to find angles?

Your new information complicates things a bit. I will have to amend some of my prior statements. First, the angles are not given as simple bearing angles. A different orientation is being used. Second, there is a bend in the "2nd leg"; i.e., it's actually two legs that are almost in line.

Do you know if there is some reason for that 2nd leg to be bent? I notice your drawing specifies "iron found" at each of the corners. Could the pipe be an erroneously placed marker? If it is an actual marker, why not the same "iron found" as at the corners??? Seems odd.

Anyway, let's address your question about angles at the four major corners.

Let's start in the middle of the cul-de-sac. If you extend the two lines that intersect the edge of the cul-de-sac into the cul-de-sac, they will intersect and form an angle. The angle formed will be

50° 10' 42" + 03° 27' 19" = 53° 38' 01"

Hopefully, you know how to deal with "degrees, minutes, seconds" angle measurements. There are 60" (60 seconds) in 1' (one minute), 60' (60 minutes) in 1° (one degree), and 360° in a circle. In the above addition, 42" + 19" = 61" = 1' 01". The 1' is added to the other minute values: 1' + 10' + 27' = 38'. Make sense?

Moving on to the "iron found" at legs 1 and 2 intersection, we have

180° - (50° 10' 42" - 01° 23' 27") = 180° - (49° 70' 42" - 01° 23' 27")

180° - (49° 70' 42" - 01° 23' 27") = 180° - (48° 47' 15")

180° - (48° 47' 15") = (179° 59' 60") - (48° 47' 15")

(179° 59' 60") - (48° 47' 15") = 131° 12' 45"

***

With the above examples, are you able to proceed on your own? Was this problem given as a homework assignment? If so, what exactly are you studying? What class and grade are you in? As I suggested above, lay a protractor on the drawing and measure the angles. You can't read them down to the nearest second, but the nearest degree should be right: about 53 degrees in the cul-de-sac and 131 degrees at the first "iron". The protractor will give you a quick check on the accuracy of your calculations.

Hope that helps.