Question

1. what is the m∠lnm?

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of the central angle that subtends the same arc.

Step2: Identify the central and inscribed angles

The central angle \(\angle LPM = 108^{\circ}\), and the inscribed angle \(\angle LNM\) subtends the same arc \(\overset{\frown}{LM}\).

Step3: Calculate the measure of \(\angle LNM\)

By the inscribed - angle theorem, \(m\angle LNM=\frac{1}{2}m\angle LPM\).
Substitute \(m\angle LPM = 108^{\circ}\) into the formula: \(m\angle LNM=\frac{1}{2}\times108^{\circ}\).
\(m\angle LNM = 54^{\circ}\)

Answer:

\(54^{\circ}\)