To calculate the angles you have to star with the uper triangle FCD
The angle with measure 157º and the inner angle of vertex D are supplementary, this means that their measures add up to 180º
180º = 157º+D
D= 180-157=23º
Now that we know the inner angle of D, we can calculate the angle F
Sum of al inner angles of a triangle is 180º, so
180º= C+D+F
F= 180-42-23
F= 115º
Now you can link angles C and B with a Z shaped line, this indicates that they are alternate angles, these type of angles are congruent, so
C=B=42º
Finally you can calculate A by either applying you knowledge of the summ of the inner angles of the triangle or applying the concept of alternate angles.
Angle A can be linked with a Z shaped line to the iiner angle D, meaning that A=D= 23º
Or you can
180º= A+F+B
180º= A+42+115
180º=23º
Angles
A= 23º
F=115º
B=42º