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To find the measure of arc \( LJK \) in the given circle, we can use the information provided in the diagram:

1. **Understanding the Diagram**:
   - \( K \) is a point on the circumference of the circle.
   - \( JKL \) is a triangle inscribed in the circle with \( K \) at the top.
   - The angle at \( K \) is marked as \( 90^\circ \).
   - \( J \) and \( L \) are endpoints of the arc \( LJK \).

2. **Key Properties**:
   - When an angle is inscribed in a circle and the angle is \( 90^\circ \), it implies that the arc subtended by this angle is a semicircle. This is because an angle of \( 90^\circ \) at the circumference subtends an arc that is half the circle.

3. **Arc \( LJK \)**:
   - The arc \( LJK \) subtended by the angle \( \angle JKL = 90^\circ \) must be a semicircle.
   - A semicircle in any circle measures \( 180^\circ \).

Thus, the measure of arc \( LJK \) is \( \boxed{180^\circ} \).

Would you like further details or have any questions?

### Related Questions:
1. What is the measure of the arc opposite to arc \( LJK \)?
2. How would the arc measure change if \( \angle JKL \) were \( 120^\circ \) instead of \( 90^\circ \)?
3. What is the relationship between the central angle and the arc it subtends?
4. How can the measure of an arc be calculated if the angle is not at the circumference?
5. What is the significance of the angle at the center of a circle compared to an inscribed angle?

### Tip:
Remember, an inscribed angle in a circle is always half the measure of the arc it subtends. This property is crucial for solving many circle-related geometry problems.

Learn how to find the measure of arc LJK in a circle using the inscribed angle theorem and semicircle theorem. This problem involves understanding circle geometry and properties of angles in circles.

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