Answer :

Let's solve the given math problems step-by-step.

1. Expression: [tex]\( 1 - 80 + 77 \)[/tex]

Step-by-step solution:
- First, subtract [tex]\( 80 \)[/tex] from [tex]\( 1 \)[/tex]:
[tex]\[ 1 - 80 = -79 \][/tex]
- Then, add [tex]\( 77 \)[/tex] to the result:
[tex]\[ -79 + 77 = -2 \][/tex]

Result: The value of [tex]\( 1 - 80 + 77 \)[/tex] is [tex]\(-2\)[/tex].

2. Expression: [tex]\( 77 + 60 \)[/tex]

Step-by-step solution:
- Simply add [tex]\( 77 \)[/tex] and [tex]\( 60 \)[/tex]:
[tex]\[ 77 + 60 = 137 \][/tex]

Result: The value of [tex]\( 77 + 60 \)[/tex] is [tex]\( 137 \)[/tex].

3. Expression: [tex]\( -105 - (-122) \)[/tex]

Step-by-step solution:
- When subtracting a negative number, it is equivalent to adding it:
[tex]\[ -105 - (-122) = -105 + 122 \][/tex]
- Now add [tex]\( -105 \)[/tex] and [tex]\( 122 \)[/tex]:
[tex]\[ -105 + 122 = 17 \][/tex]

Result: The value of [tex]\( -105 - (-122) \)[/tex] is [tex]\( 17 \)[/tex].

4. Expression: [tex]\( 185 - (-154) \)[/tex]

Step-by-step solution:
- When subtracting a negative number, it is equivalent to adding it:
[tex]\[ 185 - (-154) = 185 + 154 \][/tex]
- Now add [tex]\( 185 \)[/tex] and [tex]\( 154 \)[/tex]:
[tex]\[ 185 + 154 = 339 \][/tex]

Result: The value of [tex]\( 185 - (-154) \)[/tex] is [tex]\( 339 \)[/tex].

To summarize:

1. The result of [tex]\( 1 - 80 + 77 \)[/tex] is [tex]\(-2\)[/tex].
2. The result of [tex]\( 77 + 60 \)[/tex] is [tex]\( 137 \)[/tex].
3. The result of [tex]\( -105 - (-122) \)[/tex] is [tex]\( 17 \)[/tex].
4. The result of [tex]\( 185 - (-154) \)[/tex] is [tex]\( 339 \)[/tex].