angles

Question

Given: angle CAR is a right angle

the measure of angle CAT = 37 degrees, 66 minutes, 10 seconds

Find: the measure of angle RAT

 

Answer 1

From Figure ∠CAR= ∠CAT + ∠RAT

∠RAT = ∠CAR - ∠CAT

∠CAT = 37 degrees, 66 minutes, 10 seconds

60 seconds = 60” = 1 minute = 1’

60 minutes = 60’ = 1 degree 

Write ∠CAT  angle as

=37 degrees + (60 minutes) + 6 minutes + 10 seconds

=37 degrees + 1 degree + 6 minutes + 10 seconds

=38 degrees + 6 minutes + 10 seconds

A right angle is equal to 90 degrees, so,∠CAR = 90º

Write 90º as 89 degrees + 59 minutes + 60 seconds

Now find the  ∠RAT

∠RAT = ∠CAR - ∠CAT

∠RAT = (89 degrees + 59 minutes + 60 seconds) - (38 degrees + 6 minutes + 10 seconds)

∠RAT = 51 degrees, 53 minutes, 50 seconds.