PART A. a=123, b=123, c=57
The angle that is labeled as 123 degrees is an alternate interior angle to b. Alternate interior angles are congruent, meaning that b=123.
a and b are vertical angles. Vertical angles are congruent, meaning that the angles for angle a and angle b are the same. So a=123.
C is a linear pair angle. Meaning that 123 and angle c equals to 180 degrees.
So you do 180-123 which would equal to 57.
PART B. d=98, e=98, f=98
The angle with the degree of 82 and angle f are linear pair angles. Meaning that when added together, they equal to 180.
So you do 180-82, which would equal to 98. F=98.
Angles d and f are corresponding angles. Corresponding angles are congruent. So if f equals to 98, then d also equals to 98.
Angles d and e are vertical angles. Vertical angles are congruent. So angle e also equals to 98 degrees.
PART C. g=75
The angle with the degree of 75 are alternate interior angles to angle g. Alternate interior angles are congruent. Meaning that g equals to 75 degrees.