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

Answer 1

To find the measure of angle KIJ, we first need to find the values of x by setting the arc length equations equal to each other:

13x - 10 = 7x - 10
6x = 0
x = 0

Now that we have found the value of x, we can substitute it back into either of the arc length equations to find the actual lengths of arc KJ and arc JI:

arc KJ = 13(0) - 10 = -10
arc JI = 7(0) - 10 = -10

Since both arc KJ and arc JI have lengths of -10, this means that the arc KJ and arc JI together form a semicircle. The angle subtended by a semicircle is always 180 degrees. Therefore, m∠KIJ = 180 degrees.