Answer:
a = 55°
d + c = 180°
130° + c = 180°
c = 180° - 130°
c = 50°
a + b + c = 180°
a + 75° + 50° = 180°
a = 180° - 75° - 50°
a = 55°
(This is the longer method.)
You can also apply the Opposite Angle Theorem, where angles that are positioned in opposing sides have equal angles. Since angle a and b is the opposite angle of d, then, a+b = d.
a + b = d
a + 75° = 130°
a = 130° - 75°
a = 55°
(This is the simplest answer.)
