Answer:
64.7 degrees
Explanation:
First, you need to find the measure of angle KJL, which is the central angle subtended by arc MN. You can use the fact that the opposite angles of a cyclic quadrilateral (a quadrilateral inscribed in a circle) are supplementary (add up to 180 degrees). Therefore, m∠KJL = 180 - m∠KLM = 180 - 67 = 113 degrees.
Next, you need to use the fact that the measure of an arc is proportional to the measure of the central angle that subtends it. The proportionality constant is 2π360, which is the ratio of the total degrees in a circle to the total radians in a circle. Therefore, measure of arc MN = 2π360 × m∠KJL = 2π360 × 113 ≈ 64.7 degrees.