If arc KJ=13x-10 and arc JI=7x-10, then find the m <KIJ.
-80 degrees
-60 degrees
-10 degrees
120 degrees
To find the measure of angle KIJ, we can use the fact that the sum of the measures of the three angles formed by the intercepted arc is always 180 degrees.
Therefore, we have:
m< KIJ = m< KJ + m< JI
m< KIJ = (13x-10) + (7x-10)
m< KIJ = 20x - 20
Since the sum of the three angles KIJ, KIJ, and IJ is 180 degrees, we have:
20x - 20 = 180
20x = 200
x = 10
Now we can plug in x=10 into the formula for angle KIJ:
m< KIJ = 20(10) - 20
m< KIJ = 200 - 20
m< KIJ = 180 degrees
Therefore, the measure of angle KIJ is 180 degrees.