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
𝑚
∠
𝐾
𝐼
𝐽
=
37
degrees, then what is the measure of arc IJ
𝐼
𝐽
?

(1 point)
Responses

74 degrees
74 degrees

53 degrees
53 degrees

106 degrees
106 degrees

143 degrees
143 degrees

Answer 1

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 the semicircle KI is 180°, and arc IJ = 180° − 74° = 106°.