Question

given circle k with chords (overline{lj}), (overline{ln}), (overline{mj}), and (overline{mn}), and (overleftrightarrow{olp}) tangent to k at point l. find an angle that measures half as much as (overset{\frown}{lm}).

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc.

Step2: Identify the inscribed angle for arc \(LM\)

The inscribed angle that intercepts arc \(LM\) is \(\angle LJM\) (or \(\angle LNM\)). By the inscribed - angle theorem, if the measure of arc \(LM\) is \(m\overset{\frown}{LM}\), then \(m\angle LJM=\frac{1}{2}m\overset{\frown}{LM}\) and \(m\angle LNM = \frac{1}{2}m\overset{\frown}{LM}\)

Answer:

\(\angle LJM\) (or \(\angle LNM\))