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### Problem:
We are asked to find the measure of arc \( JKM \) if \( m \angle KLM = 35^\circ \).

### Information from the image:
1. The circle is centered at \( L \).
2. \( JKM \) is a major arc of the circle.
3. \( m \angle KLM = 35^\circ \) (Given).

### Key Concepts:
- **Central Angle Theorem**: The measure of an arc in a circle is equal to the measure of the central angle that intercepts the arc.
- \( \angle KLM \) is a central angle and intercepts the arc \( KM \). Hence, the measure of arc \( KM \) is equal to \( m \angle KLM \), which is \( 35^\circ \).
- The total angle around a circle is \( 360^\circ \), so the arc \( JKM \) is the remaining part of the circle after subtracting the measure of arc \( KM \).

### Calculation:
The measure of arc \( JKM \) is:
\[
\text{Measure of arc } JKM = 360^\circ - \text{Measure of arc } KM
\]
\[
\text{Measure of arc } JKM = 360^\circ - 35^\circ = 325^\circ
\]

### Final Answer:
The measure of arc \( JKM = 325^\circ \).

Would you like any further details or explanations on this? 

Here are some related questions you can explore:
1. What is the relationship between central angles and their intercepted arcs?
2. How do you calculate the length of an arc given its central angle?
3. Can an inscribed angle help in finding the arc's measure?
4. How can we find the measure of an arc if the angle is subtended by a diameter?
5. How does the central angle theorem apply to minor and major arcs?

**Tip:** When working with arcs, always check whether the angle given is central or inscribed. This distinction is key for solving problems involving circles.

Find the measure of arc JKM if m∠KLM = 35°.

Solve a circle geometry problem where we find the measure of arc JKM when the central angle ∠KLM is 35°. This solution covers key concepts such as the Central Angle Theorem and the relationship between arcs and angles in a circle. Suitable for students in Grades 9-11.

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