OK, you forced me to derive it. We will initially solve for C.

Follow carefully.

C= angle adjacent the angle we are looking for.
A= included angle at first incidence (per your definition)
B= included angle at second incidence (per your definition)
I= angle of first incidence (relative to mirror)
J= angle of second incidence (relative to mirror)

C=180-(A+B)

A=180-2I
B=180-2J
J=180-I-50

Substitute in formula for C:

180-((180-2I)+(180-2J))

180-((180-2I)+(180-2(180-I-50)))

Solve for C:

180-180+2I-180+360-2I-100=80

The angle we want is 180-C.

180-80=100.