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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If arc KJ=13x−10
and arc JI=7x−10
, then find the m∠KIJ
.

(1 point)

80 degrees

120 degrees

10 degrees

60 degrees

Answer 1

If arcs KJ and JI form a semicircle, then
(13x − 10) + (7x − 10) = 180
20x − 20 = 180
x = 10.

Then arc KJ = 13(10) − 10 = 120°, so the inscribed angle ∠KIJ = 1/2·(arc KJ) = 60°.

Answer: 60 degrees.