if arc KJ=13x-10 and arc JI=7x-10 then find the m∠KIJ
80,60,10,120
In a circle, the measure of an inscribed angle is equal to half the measure of its intercepted arc.
Therefore, m∠KIJ = (13x - 10 + 7x - 10) / 2
m∠KIJ = (20x - 20) / 2
m∠KIJ = 10x - 10
Since the angles of a triangle add up to 180 degrees, we can also say that:
10x - 10 + 13x - 10 + 7x - 10 = 180
30x - 30 = 180
30x = 210
x = 7
Substitute x = 7 into m∠KIJ = 10x - 10:
m∠KIJ = 10(7) - 10 = 70 - 10 = 60
Therefore, the measure of ∠KIJ is 60 degrees.