Question

Find each value or measure. Assume that all segments that appear to be tangentare tangent. Find JLK

Answer 1

Answer

Angle JLK = 31°

Explanation

To answer this, we will use the tangent-chord theorem.

So, the intercepted arc JNL has an angle 298°

Then, we can solve for the tangent chord angle next to it, Angle JLM first by saying

Angle JLM = (Intercepted arc JNL)/2

Angle JLM = (298°/2)

Angle JLM = 149°

Then, we can see that Angle JLM and Angle JLK lie on the same straight line, KLM.

Sum of angles on a straight line is 180°.

Angle JLK + Angle JLM = 180°

Angle JLK + 149° = 180°

Angle JLK = 180° - 149°

Angle JLK = 31°

Hope this Helps!!!