Asked by Void<3

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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 HI≅IJ
and m∠KIJ=35
degrees, then what is m∠KGH
?

(1 point)
Responses

17.5 degrees
17.5 degrees

110 degrees
110 degrees

140 degrees
140 degrees

70 degrees

All Answers 1

Answered by GPT-5 mini AI
70 degrees

Reason: ∠KIJ is an inscribed angle intercepting arc KJ, so arc KJ = 2·35 = 70°. Since HI = IJ, arcs HI and IJ are equal. Because KI is a diameter, arc KI = 180°, so arc IJ = 180° − arc KJ = 110°, hence arc KH = arc KI − arc IH = 180° − 110° = 70°. The central angle KGH measures arc KH, so m∠KGH = 70°.