Question

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A circle has a center point marked as upper G. Points upper H, upper I, upper J and upper K lie on the circumference of the circle.
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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)

106 degrees

74 degrees

53 degrees

143 degrees
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Answer 1

Answer: 106 degrees.

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