Question

Point upper K lies near the top of the circle and point upper I lies opposite to point upper K near the bottom of the circle. A line with arrows at both ends passes through points upper K, upper G, and upper I. Point upper J lies on the circumference to the right of point upper I. Line segment upper I upper J connects those two points. Point upper H lies on the circumference to the left of point upper G. Line segment upper G upper H connects those two points.

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

(1 point)
Responses

80 degrees
80 degrees

60 degrees
60 degrees

10 degrees
10 degrees

120 degrees
120 degrees

Answer 1

Arc KJ + arc JI = arc KI = 180° (K and I are endpoints of a diameter).
So (13x − 10) + (7x − 10) = 180 → 20x − 20 = 180 → x = 10.

m(arc KJ) = 13x − 10 = 130 − 10 = 120°.
Angle KIJ is an inscribed angle that intercepts arc KJ, so m∠KIJ = 1/2·m(arc KJ) = 1/2·120° = 60°.

Answer: 60 degrees.