**Topic: Geometry - Circle and Angles****Problem Statement:**In circle \( J \) with \( \angle HLK = 37^\circ \), find the measure of minor arc \( HK \).**Diagram Explanation:**The diagram presents a circle with the center labeled as \( J \). Points \( H \), \( L \), and \( K \) are marked on the circumference of the circle. The angle \( \angle HLK \) is indicated within the circle, intersecting the arc \( HK \).**Solution Steps:**To solve the problem, we can use the relationship between the central angle and the arc in a circle. Here are the steps:1. The angle \( \angle HLK \) is given as \( 37^\circ \).2. Note that \( \angle HLK \) is the inscribed angle that intercepts the minor arc \( HK \).3. Recall the property of circles: the measure of an inscribed angle is half the measure of the intercepted arc.4. Let \( m \) be the measure of the minor arc \( HK \).5. According to the property: \( \angle HLK = \frac{1}{2} \times m \).6. Substitute \( \angle HLK = 37^\circ \) into the equation: \( 37^\circ = \frac{1}{2} \times m \).7. Solve for \( m \): \[ m = 2 \times 37^\circ \] \[ m = 74^\circ \]So, the measure of the minor arc \( HK \) is \( 74^\circ \).

Name: **Topic: Geometry - Circle and Angles****Problem Statement:**In circl
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: **Topic: Geometry - Circle and Angles****Problem Statement:**In circle \( J \) with \( \angle HLK = 37^\circ \), find the measure of minor arc \( HK \).**Diagram Explanation:**The diagram presents a circle with the center labeled as \( J \). Points