Question

m∠knm = \frac{1}{2}
= \frac{1}{2}
= \frac{1}{2}(160 - 96)
= \frac{1}{2}64
= 32
(\text{m}\overparen{kn}-\text{m}\overparen{lk}) (160 - (180 - 94)) 24 84 (\text{m}\overparen{km}-\text{m}\overparen{lk}) 48 (160 - (360 - 264)) 42
(\text{m}\overparen{kn}-\text{m}\overparen{lm})

Explanation:

Step1: Identify the formula for the measure of an inscribed - angle related to arc measures

The measure of an inscribed - angle is half the difference of the measures of the intercepted arcs. Here, \(m\angle KNM=\frac{1}{2}(m\overparen{KM}-m\overparen{LK})\).

Step2: Calculate the difference of the arc measures

We are given that \(m\overparen{KM} = 160^{\circ}\) and \(m\overparen{LK}=96^{\circ}\), so \(m\overparen{KM}-m\overparen{LK}=160 - 96=64^{\circ}\).

Step3: Calculate the measure of the angle

Since \(m\angle KNM=\frac{1}{2}(m\overparen{KM}-m\overparen{LK})\), substituting the value of \(m\overparen{KM}-m\overparen{LK} = 64^{\circ}\), we get \(m\angle KNM=\frac{1}{2}\times64^{\circ}=32^{\circ}\).

Answer:

\(m\angle KNM=\frac{1}{2}(m\overparen{KM}-m\overparen{LK})\), \(32^{\circ}\)