Find the KOM angle if the degree measures of the arc are MN = 124 ° and the arc is KN = 180 °.

If O is the center of the circle, and K, M and N are points on the circle, then the arcs KM, KN and NM formed by these points and the corresponding degree measures, as well as the values of the angles MON, KON and KOM corresponding to them, together form 360⁰:

This means that to find the value of the PTO angle, you need to subtract from the 360⁰ degree measures of both arcs:

360⁰ – 124⁰ – 180⁰ = 180⁰ – 124⁰ = 56⁰.

Answer: the KOM angle is 56⁰.