To find the measure of arc IJ given that m∠KIJ = 37 degrees, we can use the relationship between the angle and the arc it subtends in a circle.
In a circle, the measure of the angle formed by two lines from the center of the circle to the points on the circumference (the angle's vertex is on the circle itself) is half the measure of the arc it subtends. However, because angle KIJ is not at the center, we need to consider inscribed angles.
The measure of the inscribed angle is half the measure of the arc it intercepts:
\[ m\angle KIJ = \frac{1}{2} m\text{arc } IJ \] Given that m∠KIJ = 37 degrees:
\[ 37 = \frac{1}{2} m\text{arc } IJ \]
To solve for m arc IJ, multiply both sides by 2:
\[ m\text{arc } IJ = 74 \text{ degrees} \]
So the measure of arc IJ is:
\[ \text{74 degrees} \]
The correct response is 74 degrees.