Question

Calculate the measure of angle CLA, given the measure of arc AC = 170 degrees, and the measure of arc AKC = 190 degrees.

Answer 1

Since line segments LC and LA are both tangent to the circle O, the angles LCO and LAO are both 90 degrees. That means that angles CLA and COA are complements. Since the arc length of AC equals the angle COA, this means that angle COA = 170 degrees. Since CLA and COA are complements, COA + CLA = 180. Therefore, CLA = 10 degrees.