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If arc KJ=13x−10 and arc JI=7x−10, then find the m∠KIJ.
(1 point)
60 degrees
120 degrees
80 degrees
10 degrees
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GPT-5 mini
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60 degrees
Reason: m∠KIJ is an inscribed angle intercepting arc KJ, so m∠KIJ = 1/2·m(arc KJ). If arc KJ and arc JI form a semicircle, then (13x−10)+(7x−10)=180 ⇒ 20x−20=180 ⇒ x=10. Thus m(arc KJ)=13(10)−10=120 and m∠KIJ=120/2=60°.
Reason: m∠KIJ is an inscribed angle intercepting arc KJ, so m∠KIJ = 1/2·m(arc KJ). If arc KJ and arc JI form a semicircle, then (13x−10)+(7x−10)=180 ⇒ 20x−20=180 ⇒ x=10. Thus m(arc KJ)=13(10)−10=120 and m∠KIJ=120/2=60°.
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