SOLUTION: how do i do this? m∠ROS = 20 deg 15' 40", m∠SOT = 10 ° 12' 30" m∠ROT =

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Degrees may be further divided into minutes and seconds, but that division is not as universal as it used to be.
Each degree is divided into 60 equal parts called minutes.
Each minute is further divided into 60 equal parts called seconds.

m∠ROS = 20° 15' 40", m∠SOT = 10 ° 12' 30"

m∠ROT=180° - (m∠ROS + m∠SOT)
m∠ROT=180° - (20° 15' 40" + 10 ° 12' 30")
m∠ROT=180° - (30° 27' 70" )...............70"=1' 10"
m∠ROT=180° - (30° 28' 10" )..
m∠ROT=180° - (30° 28' 10" ).......take 1° from 180° and convert to minutes, then take one minute and convert to seconds
m∠ROT=179° 59' 60" - 30° 28' 10" ..now subtract degrees from degrees, minutes from minutes, and seconds from seconds
m∠ROT=(179°-30°) (59'-28' ) (60" -10")
m∠ROT=149° 31' 50"