Question

Use the image to answer the question.

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

Answer 1

70 degrees

Reason: Let arc HI = arc IJ = x. Because KI is a diameter, arc KH + arc HI = 180°, so arc KH = 180 - x. The inscribed angle ∠KIJ intercepts arc KJ = 180 - x, so 35 = 1/2(180 - x) ⇒ 180 - x = 70. Hence arc KH = 70°, and the central angle ∠KGH = 70°.