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The problem shows a circle with center \( A \), and triangle \( MKJ \) is inscribed in the circle. Given that the measure of \( \angle MKJ \) is \( 40^\circ \), we are asked to find the measure of the arc \( MK \).

Here’s how we can solve it:

### Step-by-Step Solution:
1. **Central Angle Theorem:**
   In a circle, the angle subtended by an arc at the center of the circle is twice the angle subtended by the same arc at any point on the circumference.

2. **Applying this Theorem:**
   - \( \angle MKJ \) is an inscribed angle that subtends the arc \( MK \).
   - Therefore, the measure of the arc \( MK \) is twice the measure of \( \angle MKJ \).

3. **Calculation:**
   - The given measure of \( \angle MKJ \) is \( 40^\circ \).
   - So, the measure of arc \( MK \) is \( 2 \times 40^\circ = 80^\circ \).

Thus, the measure of arc \( MK \) is \( \boxed{80^\circ} \).

Would you like more details or have any questions?

### Related Questions:
1. What is the relationship between central angles and inscribed angles?
2. How do you calculate the measure of an arc given a central angle?
3. How would the solution change if the given angle was a central angle instead?
4. What is the difference between a minor arc and a major arc?
5. Can you find the measure of arc \( JK \) if \( \angle MKJ = 40^\circ \)?

### Tip:
Always remember the Central Angle Theorem: the central angle is twice any inscribed angle subtended by the same arc!

The circle has center A. If the measure of angle MKJ is 40°, find the measure of the arc MK in degrees.

Learn how to calculate the measure of the arc MK in a circle with center A, given that the angle MKJ is 40°. This problem utilizes the Central Angle Theorem, which states that the arc subtended by an inscribed angle is twice the angle. Suitable for Grades 8-10.

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