Question

1. ( m widehat{j k}= ) 5. ( m widehat{k n m}= ) 6. ( m widehat{m j l}= )

Explanation:

Step1: Find the measure of \( \angle JPK \)

Assume the circle is divided into 6 equal - part angles (since there are 6 radii shown). The total measure of a circle is \( 360^{\circ} \).
If the circle is divided into \( n = 6\) equal - part angles, then each central angle \( \theta=\frac{360^{\circ}}{n}\).
For \( n = 6\), \( \theta=\frac{360^{\circ}}{6}=60^{\circ}\). So, \( m\overset{\frown}{JK}=60^{\circ}\) (the measure of an arc is equal to the measure of its central angle).

Step2: Find the measure of \( \overset{\frown}{KNM}\)

\( \overset{\frown}{KNM}\) is a major arc. The measure of a major arc is \( 360^{\circ}\) minus the measure of the corresponding minor arc.
The minor arc corresponding to \( \overset{\frown}{KNM}\) is \( \overset{\frown}{KL}\). Since each central angle is \( 60^{\circ}\), \( m\overset{\frown}{KL} = 60^{\circ}\).
\( m\overset{\frown}{KNM}=360^{\circ}-60^{\circ}=300^{\circ}\)

Step3: Find the measure of \( \overset{\frown}{MJL}\)

\( \overset{\frown}{MJL}\) is composed of 4 central angles. Each central angle is \( 60^{\circ}\).
Using the formula \( m\overset{\frown}{MJL}=4\times60^{\circ}=240^{\circ}\)

Answer:

1. \( 60\)
2. \( 300\)
3. \( 240\)