Transcribed Image Text:**Understanding Central Angles and Arc Measures**
In this lesson, we will explore the relationship between central angles and arc measures in a circle.
### Example Problem:
#### 2.
In the diagram above, we have a circle with center \(N\). Points \(J\), \(K\), \(L\), and \(M\) lie on the circumference of the circle, forming various segments and arcs as indicated. The measure of \(\angle JNM\) is given as \(21^\circ\).
Your task is to determine the following measurements based on the given diagram:
1. \(m \overarc{JK} =\) ______
2. \(m \angle JNM =\) ______
3. \(m \overarc{KL} =\) ______
4. \(m \angle JKN =\) ______
5. \(m \overarc{JKL} =\) ______
Use the diagram to find the values of the arc measures and angles.
#### Details and Explanations:
1. **Arc \(JK\)** - This is the minor arc from point \(J\) to point \(K\) on the circle. The measurement of an arc is equivalent to the measure of its corresponding central angle.
2. **Angle \(\angle JNM\)** - This is the angle subtended at the center \(N\) by the line segments \(JN\) and \(NM\). It is already provided as \(21^\circ\).
3. **Arc \(KL\)** - This arc lies between points \(K\) and \(L\) on the circle. Like arc \(JK\), it depends on the central angle corresponding to points \(K\) and \(L\).
4. **Angle \(\angle JKN\)** - This angle involves points \(J\), \(K\), and \(N\). The value needs to be inferred based on given arc measures.
5. **Arc \(JKL\)** - This arc includes points \(J\), \(K\), and \(L\) and covers a larger portion of the circle, combining the minor arcs between these points.
### Explanation of Diagram:
- **Circle with Center \(N\)**: The circle is denoted with center \(N\). Radii are drawn from \(N\) to points \(J\), \(K\), \(
Figure in plane geometry formed by two rays or lines that share a common endpoint, called the vertex. The angle is measured in degrees using a protractor. The different types of angles are acute, obtuse, right, straight, and reflex.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.
In the diagram above, we have a circle with center \(N\). Points \(J\), \(K\), \(L\), and \(M\) lie on the circumference of the circle, forming various segments and arcs as indicated. The measure of \(\angle JNM\) is given as \(21^\circ\).
Your task is to determine the following measurements based on the given diagram:
1. \(m \overarc{JK} =\) ______
2. \(m \angle JNM =\) ______
3. \(m \overarc{KL} =\) ______
4. \(m \angle JKN =\) ______
5. \(m \overarc{JKL} =\) ______
Use the diagram to find the values of the arc measures and angles.
#### Details and Explanations:
1. **Arc \(JK\)** - This is the minor arc from point \(J\) to point \(K\) on the circle. The measurement of an arc is equivalent to the measure of its corresponding central angle.
2. **Angle \(\angle JNM\)** - This is the angle subtended at the center \(N\) by the line segments \(JN\) and \(NM\). It is already provided as \(21^\circ\).
3. **Arc \(KL\)** - This arc lies between points \(K\) and \(L\) on the circle. Like arc \(JK\), it depends on the central angle corresponding to points \(K\) and \(L\).
4. **Angle \(\angle JKN\)** - This angle involves points \(J\), \(K\), and \(N\). The value needs to be inferred based on given arc measures.
5. **Arc \(JKL\)** - This arc includes points \(J\), \(K\), and \(L\) and covers a larger portion of the circle, combining the minor arcs between these points.
### Explanation of Diagram:
- **Circle with Center \(N\)**: The circle is denoted with center \(N\). Radii are drawn from \(N\) to points \(J\), \(K\), \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F467ecbdb-fd5b-4b4c-ab67-30d508e676d8%2F094e4460-b90d-441d-acc1-2ae28cdbcc58%2Fdv87bz6_processed.jpeg&w=3840&q=75)
