Explanation:
always remember : the sum of all angles in a triangle is 180°. always. for any triangle.
and also : every degree has 60 minutes, and every minute has 60 seconds.
96.
we see an isoceles triangle (the 2 baseline angles are the same, so both legs must be equally long).
so,
180 = a + a + 30°24'12" = 2a + 30°24'12"
2a = 180 - 30°24'12" = 180 - 31 + (60-25) + (60-12) =
= 149°35'48"
a = (149/2)°(35/2')(48/2)" =
= 74.5°17.5'24" = 74°30' + 17'30" + 24" =
= 74°47'54"
remember, we apply the "carry-over" of a normal subtraction by subtracting one more unit from the larger units than we have to, then add this unit again by a full unit expressed in the smaller size. and so on, until we are at the end.
so, 180 - 31 (instead of 30), then we add this degree via 60 minutes and subtract 25 minutes (instead of 24), then we add this minute via 60 seconds and subtract the seconds.
98.
180 = a + 90° + 61°1'48"
a = 180° - 90° - 61°1'48" = 90 - 61°1'48" =
= 90° - 62° + (60-2)' + (60-48)" =
= 28°58'12"