Online protractor

The complement and supplement are the two relationships that come up constantly and get mixed up just as often. Complementary angles add to 90 degrees — the two non-right angles in any right triangle are complementary. Supplementary angles add to 180 — angles on a straight line, and the co-interior angles between parallel lines. A useful way to keep them apart is alphabetical: complementary comes first and pairs with the smaller number.

Radians are given because most programming and all calculus use them. A radian is the angle where the arc equals the radius, which makes a full turn 2π rather than an arbitrary 360. The 360 is Babylonian and survives because it divides evenly by so many numbers — 2, 3, 4, 5, 6, 8, 9, 10, 12 and more — which is genuinely convenient for a protractor and useless for mathematics. Every trigonometric function in JavaScript, Python and C takes radians, which is why Math.sin(90) returns −0.89 rather than 1.

For measuring a real object against the screen the same caveat applies as to an on-screen ruler: angles are more forgiving than lengths, because an angle does not depend on scale — a 30-degree angle is 30 degrees at any size. So a screen protractor is actually more trustworthy than a screen ruler, as long as you are looking straight at the display rather than from an angle yourself.