Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
![### Geometric Problem involving Angles in a Circle
**Problem Statement:**
In the diagram provided, we have a circle with center at point \(N\) and four points \(K\), \(L\), \(J\), and \(M\) on the circumference. The measurements given are:
- \(\angle KJM = 53^\circ\)
- \(\angle KLM = 65^\circ\)
You are required to determine the measure of \(\angle JKL\).
**Diagram Explanation:**
The diagram shows a circle with center \(N\) and four points on the circumference: \(K\), \(L\), \(J\), and \(M\). There are two marked angles, \(\angle KJM\) which is \(53^\circ\) and \(\angle KLM\) which is \(65^\circ\). The objective is to find the measure of \(\angle JKL\).
**Open-Ended Statement:**
To find \(m\angle JKL\), use your knowledge of the properties of angles in a circle, particularly the relationships between inscribed angles and the arcs they intercept.
**Solution Box:**
\[ m\angle JKL = \underline{ \hspace{3cm} } \]
This exercise provides practice in solving geometric problems involving circles and understanding the measures of angles subtended by the same arc.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e6d795f-fdb9-4357-aaec-e7e4d81017d7%2F1b57ce1a-dd14-4e2b-941a-d8d798c1024c%2Fx92kze9_processed.jpeg&w=3840&q=75)
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