Answer: Two angles are complementary when they add up to 90°
then, doing all the options:
A) 50° + 41° = 91°, so this angles are non complementary.
B) 100° + 80° = 180°, so this aren't complementary, but they are Supplementary (because their addition is 180°) angles.
C) 77° + 13° = 90°, si this angles are complementary
D) 35° + 10° = 45°, this pair is not complementary.
So the only correct answer is C.