2Angular MeasurementCircles are divided into 360 equal parts, each being a degree.Each of these degrees can be evenly divided into 60 equal parts. These parts are called minutes.These minutes can be evenly divided into 60 equal parts. These parts are called minutes.
3Angular Measurement 1 Circle = 360 Degrees ( 360° ) 1 Degree ( 1° ) = 1/360th of a Circle1 Degree ( 1°) = 60 Minutes ( 60' )1 Minute ( 1' ) = 1/60th of a Degree1 Minute ( 1') = 60 Seconds ( 60" )1 Second ( 1" ) = 1/60th of a Minute
4Angular MeasurementThe unit of degree can also be divided into either decimal or fractional parts and is referred to as decimal degrees or fractional degrees respectively.1½ Degree = 1.5 Degree ( 1.5°)87¼ Degrees = Degrees ( 87.25° )
5Angular MeasurementMinutes and seconds can each be expressed as decimal or fractional degrees.1 Minute ( 1' ) = 1/60th of a Degree = °1 Second ( 1" ) = 1/60th of a Minute = '
6Angular Measurement Change 5°25' to decimal degrees Divide the minutes by 6025 divided by 60 =Add to 5 = °5°25' = °
7Angular Measurement Change 27°52'35" to decimal degrees Divide the seconds by 60, add to minutes35 divided by 60 =Added to the 52 minutes, it becomes 'Divide the minutes by 60, add to degreesdivided by 60 = .8764Added to the 27 degrees, it becomes °27°52'35" = °
8Angular Measurement Change 47.75° to degrees, minutes, and seconds Multiply the decimal portion by 6075 x 60 = 45This decimal .75 becomes 45 minutes. Add this to the degrees.Since there isn't any decimal portion after the 45, no further work is necessary.47.75° = 47°45'
9Angular Measurement 82.3752° = 82°22'30.72" Change ° to Degrees, minutes, and secondsMultiply the decimal portion by 60x 60 = (the 22 becomes the minutes) Now add this to the degrees° = 82°22.512'Multiply the decimal minutes by 600.512 x 60 = Now add this to the degrees and minutes to become seconds.° = 82°22'30.72"
24Universal Bevel Protractor Precision angles to within 5' (0.083º)Consist of baseVernier scaleProtractor dialSliding bladeDial clamp nut
25Vernier Protractor Used to measure obtuse angle (90º-180º) Acute-angle attachment fastened to protractor to measure angles less than 90ºMain scale divided into two arcs of 180ºScale divided into 12 spaces on each side of 0If zero on vernier scale coincides with line on main: reading in degrees
26Reading a Vernier Protractor Note number of whole degrees between zero on main scale and zero on vernier scaleProceeding in same direction, note which vernier line coincides with main scale lineFourthMultiply number by 5' and add to degrees on protractor dial50º4 x 5'= 20'Reading =50º 20'
28Sine BarsUsed when accuracy of angle must be checked to less than 5 minutesConsists of steel bar with two cylinders of equal diameter fastened near endsCenters of cylinders exactly 90º to edgeDistance between centers usually 5 or 10 inches and 100 or 200 millimeters.Made of stabilized tool hardened steel
30Sine BarsUsed on surface plates and any angle by raising one end of bar with gage blocksMade 5 inch or in multiples of 5 or 100 millimeters or multiple of 100Distance between lapped cylinders.Face accurate to within in. in 5 inches or mm in 100 mm.