Question

In the circle below, K is the center, LN is a diameter, and m LM = 105°. Use this information to fill in the blanks.

105°

Give an inscribed angle

Answer 1

Since LN is a diameter, any angle inscribed in the circle and having LN as a chord will have a measure of 90 degrees. For example, angle LKN is an inscribed angle with measure 90 degrees, because it intercepts the diameter LN and its vertex K is on the circle.

Another inscribed angle is angle LNM, which is half of the central angle LKM. Since m(LKM) = 105°, m(LNM) = 52.5°.