Which of the following are measures of supplementary angles? a. 60° and 30° b. 122° and 58° c. 180° and 90° d. 45° and 45°

B) 122 and 58

Supplementary angles add to 180 degrees. In other words, they form a straight angle or a straight line when you combine them together (make sure they don't overlap and that there isn't any gap between them).

Choice B is the only pair of angles where they add to 180 since 122+58 = 180. The values in choice A and choice D add to 90; the values in choice C adds to 270.

Note: complementary angles add to 90 degrees. One way to remember "supplementary" vs "complementary" is to think "S for straight, C for corner". By "corner", I mean a 90 degree corner.

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.