We made this argument in class:

Claim: A straight angle has a relative arc of 0.5 (180 degrees)


  1. A line through a circle's center cuts the circle's circumference in half (some of you had reservations about whether this needs further arguing)
  2. A circle's circumference has a relative arc of 1 (360 degrees).
  3. Half of 360 degrees is 180 degrees.
  4. A straight angle cuts cuts in half any circle centered at its vertex
  5. THEREFORE, a straight angle has a measure of 180 degrees (a relative arc of 0.5).