Central Angle and measure of an Arc
The angle KLM is formed in one point of the circumference. To find the measure of the arc KM we need to find the measure of the central angle KOM as shown below:
The measure of the central angle KOM is twice the measure of the angle subtended in the circumference:
m∠KOM = 2m∠KLM
Therefore:
m∠KOM = 2*38°
m∠KOM = 76°
The measure of the arc KM is equal to this central angle.
mArc KM = 76°