Answer
$60^{\circ} 40' $
Work Step by Step
$89^{\circ} 38' $ - $ 28^{\circ} 58' $
$89^{\circ} 38' $ can also be written as $88^{\circ} 98' $ ( carrying 1 degree i.e. 60 minutes to the minutes column)
therefore the problem becomes-
$88^{\circ} 98' $ - $ 28^{\circ}58' $
$ 88^{\circ} 98' $
- $ 28^{\circ} 58' $
________
$ 60^{\circ} 40' $
Answer is $60^{\circ} 40' $