Chord KO and secant PL intersect at N. What is m ### Geometry Problem – Chord and Secant Intersection**Question:**4. Chord KO and secant PL intersect at N. What is the measure of angle ∠KNL?- (A) 20°- (B) 30°- (C) 60°- (D) 80°#### Diagram Explanation:The accompanying diagram illustrates a circle with center O. In the diagram:1. A chord KO intersects a secant PL at point N.2. ∠KML is marked as 60°.3. ∠PKO is marked as 100°.4. Points K, L, P, and O are placed approximately as follows: - K is on the circumference near the top-right. - L is on the extended line of PL to the top-right. - P is on the extended line of PL toward the bottom-left. - N is the point of intersection of KO and PL inside the circle.### SolutionTo find the measure of ∠KNL, recognizing the angles formed and the specific properties of the circle's chords and secants is essential. One key property of circle intersections involving chords and secants is helpful: the measure of an angle formed by two intersecting chords (or a chord and secant) is half the sum of the measures of the arcs intercepted by the angle and its vertical angle.Given:- ∠KML (intercepted arc by angle ∠KNL) = 60°.- ∠PKO (intercepted arc by the vertical angle point) = 100°.Calculating,\[ \text{∠KNL} = \frac{1}{2} \times (\text{intercepted arc measurements}) \]\[ \text{∠KNL} = \frac{1}{2} \times (100° + 60°) \]\[ \text{∠KNL} = \frac{1}{2} \times 160° \]\[ \text{∠KNL} = 80° \]**Answer:** (D) 80°

Name: Chord KO and secant PL intersect at N. What is m ### Geometry Problem
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Description: Chord KO and secant PL intersect at N. What is m ### Geometry Problem – Chord and Secant Intersection**Question:**4. Chord KO and secant PL intersect at N. What is the measure of angle ∠KNL?- (A) 20°- (B) 30°- (C) 60°- (D) 80°#### Diagram Explanation

we know that , the angle formed by two intersecting chords is equal to

Answered: 4. Chord KO and secant PL intersect at…

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4. Chord KO and secant PL intersect at N. What is mZKNL? (A) 20° (B) 30° (C) 60° (D) 80° K 60° M N. 100°

Algebra & Trigonometry with Analytic Geometry

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Chapter6: The Trigonometric Functions

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

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Chord KO and secant PL intersect at N. What is m

### Geometry Problem – Chord and Secant Intersection

**Question:**
4. Chord KO and secant PL intersect at N. What is the measure of angle ∠KNL?

- (A) 20°
- (B) 30°
- (C) 60°
- (D) 80°

#### Diagram Explanation:
The accompanying diagram illustrates a circle with center O. In the diagram:

1. A chord KO intersects a secant PL at point N.
2. ∠KML is marked as 60°.
3. ∠PKO is marked as 100°.
4. Points K, L, P, and O are placed approximately as follows:
- K is on the circumference near the top-right.
- L is on the extended line of PL to the top-right.
- P is on the extended line of PL toward the bottom-left.
- N is the point of intersection of KO and PL inside the circle.

### Solution
To find the measure of ∠KNL, recognizing the angles formed and the specific properties of the circle's chords and secants is essential. One key property of circle intersections involving chords and secants is helpful: the measure of an angle formed by two intersecting chords (or a chord and secant) is half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

Given:
- ∠KML (intercepted arc by angle ∠KNL) = 60°.
- ∠PKO (intercepted arc by the vertical angle point) = 100°.

Calculating,
\[ \text{∠KNL} = \frac{1}{2} \times (\text{intercepted arc measurements}) \]
\[ \text{∠KNL} = \frac{1}{2} \times (100° + 60°) \]
\[ \text{∠KNL} = \frac{1}{2} \times 160° \]
\[ \text{∠KNL} = 80° \]

**Answer:** (D) 80°

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