Question

Point upper K lies near the top of the circle and point upper I lies opposite to point upper K near the bottom of the circle. A line with arrows at both ends passes through points upper K, upper G, and upper I. Point upper J lies on the circumference to the right of point upper I. Line segment upper I upper J connects those two points. Point upper H lies on the circumference to the left of point upper G. Line segment upper G upper H connects those two points.

If m∠KIJ=37
degrees, then what is the measure of arc IJ
?

(1 point)
Responses

74 degrees
74 degrees

106 degrees
106 degrees

143 degrees
143 degrees

53 degrees
53 degrees
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Answer 1

∠KIJ is an inscribed angle that intercepts arc KJ, so arc KJ = 2·37° = 74°. Since K and I are endpoints of a diameter, arc KI = 180°, and arc KJ + arc JI = arc KI = 180°. Thus arc IJ = 180° − 74° = 106°.