If arc KJ = 13x-10 and arc JI = 7x-10, then find the m∠KIJ
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To find the measure of angle KIJ, we first need to find the measure of arc KI.
Arc KI is the sum of arc KJ and arc JI. So, arc KI = arc KJ + arc JI.
arc KI = (13x - 10) + (7x - 10)
arc KI = 20x - 20
Since the arc of a circle is proportional to the angle at the center of the circle, we can set up the proportion:
m∠KIJ / 360 = arc KI / 360
m∠KIJ / 360 = (20x - 20) / 360
Cross multiplying, we get:
360 * m∠KIJ = 20x - 20
Dividing by 360:
m∠KIJ = (20x - 20) / 360
m∠KIJ = x/18 - 1/18
Therefore, the measure of angle KIJ is x/18 - 1/18.