3. This is straight-forward subtraction.
... 79°57'30" - 76°42'25" = (79° -76°) + (57' -42') + (30" -25")
... = 3°15'5" . . . . difference in longitude
4. Here, you have to do a couple of rewrites. Since the given angle is "improper" in that it has more than 60 minutes, we have a choice. We can rewrite the angle to a "proper" angle with minutes and seconds less than 60, or we can do an unusual rewrite of the number we're subtracting from.
We can start with the relationship between the angles.
... ∠CAR = ∠CAT + ∠RAT
Subtracting ∠CAT, we have ...
... ∠RAT = ∠CAR - ∠CAT
... ∠RAT = 90° - 37°66'10"
In the first rewrite, we turn 1° into 60'.
... ∠RAT = 89°60' - 37°66'10"
In the second rewrite, we turn 1' into 60".
... ∠RAT = 89°59'60" - 37°66'10"
The number of minutes in the second number is larger than 59', so we "borrow" another degree to turn into minutes.
... ∠RAT = 88°119'60" - 37°66'10"
Now, we can perform the subtraction in a straightforward way.
... ∠RAT = (88°-37°) + (119'-66') + (60"-10")
... ∠RAT = 51°53'50"
5. The angle bisector divides the bisected angle into two equal parts. Because OC bisects ∠BOD, we know ...
... ∠BOC = ∠COD
... x = y+5
Because OC bisects ∠AOE, we know ...
... ∠AOC = ∠COE
... 2x-y+x = y+5+36
To solve this pair of equations, we can rewrite the second one by adding y and collecting terms.
... 3x = 2y +41
Subtracting this from 3 times the first equation gives ...
... 3(x) -(3x) = 3(y+5) -(2y+41)
... 0 = y -26
... 26 = y
... x = y +5 = 31
The values of x and y are x=31 and y=26.
