Question

If arc KJ = 13x - 10 and arc JI = 7x - 10, then find the m<KIJ
(1 point)
10 degrees
120 degrees
80 degrees
60 degrees

XZ is a diameter. The measure of the angle X is 59 degrees. What is the measure of arc XY?

Answer 1

1) 60°

Reason: arcs KJ and JI together make a semicircle, so (13x−10)+(7x−10)=180 → 20x−20=180 → x=10. Then arc KJ = 13(10)−10 = 120, and ∠KIJ is an inscribed angle intercepting arc KJ, so ∠KIJ = 1/2·120 = 60°.

2) 62°

Reason: ∠X = 59° is an inscribed angle intercepting arc YZ, so arc YZ = 2·59 = 118°. Since XZ is a diameter, arc XZ = 180°, and arc XY + arc YZ = 180°, hence arc XY = 180−118 = 62°.