**Problem Statement:**In circle N with \( m \angle MNP = 156 \) and \( MN = 10 \) units, find the length of arc MP. Round to the nearest hundredth.**Diagram Explanation:**This is a simple circle diagram with three points, M, N, and P:- N is the center of the circle.- M and P are points on the circumference of the circle.- The angle \( \angle MNP = 156^\circ \).- The radius MN is given as 10 units.The problem requires you to calculate the length of arc MP and round the answer to the nearest hundredth.**Solution Steps:**1. Determine the radius of the circle, which is given as 10 units.2. Recognize that the given angle \( \angle MNP = 156^\circ \) is the central angle subtending the arc MP.3. Use the formula for the length of an arc, \( L = \theta \cdot r \), where \( \theta \) is the central angle in radians and \( r \) is the radius.Convert the central angle from degrees to radians:\[ \theta = 156^\circ \times \frac{\pi}{180^\circ} = \frac{156\pi}{180} = \frac{13\pi}{15} \text{ radians} \]4. Calculate the arc length:\[ L = \frac{13\pi}{15} \cdot 10 \text{ units} \]\[ L = \frac{130\pi}{15} \text{ units} \]\[ L \approx 27.20 \text{ units (rounded to the nearest hundredth)} \]Thus, the length of arc MP is approximately 27.20 units.

Name: **Problem Statement:**In circle N with \( m \angle MNP = 156 \) and \
Uploaded: 2024-03-20T06:46:14.000Z
Channel: Bartleby
Description: **Problem Statement:**In circle N with \( m \angle MNP = 156 \) and \( MN = 10 \) units, find the length of arc MP. Round to the nearest hundredth.**Diagram Explanation:**This is a simple circle diagram with three points, M, N, and P:- N is the cent