Question

8 K MJK 21 mZJNM N mKL IL 1L 1L II mЈКМ MMKL M L

Answer 1

Using the central angle theorem, we know that arc JK is equal to 21° (its central angle).

Additionally, angles JNM and JNK are supplementary angles

`\begin{gathered} m\angle JNM+m\angle JNK=180 \\ m\angle JNM+21=180 \\ m\angle JNM=180-21=159 \end{gathered}`

Angle JNM measures 159°.

We know that angles JNM and KNL are equal by vertical angles, which means the arc KL measures 159° because it's the subtended arc of that central angle (KNL).

Now, arc JKM would be the sum 180° + 21° = 201°.

Arc JKM measures 201°.

At last, arc MKL would be equal to the difference 360° - 21° = 339°.

Arc MKL measures 339°.