Question

a regular pentagon jklmn is inscribed in circle g. part a what are the measures of arc jk, arc kl, arc lm, arc mn, and arc nj? show hints m arc jk = m arc kl = m arc lm = m arc mn = m arc nj = 102. m arc jk = m arc kl = m arc lm = m arc mn = m arc nj = 72. m arc jk = m arc kl = m arc lm = m arc mn = m arc nj = 52. m arc jk = m arc kl = m arc lm = m arc mn = m arc nj = 82.

Explanation:

Step1: Recall circle - arc property of regular polygon

For a regular polygon inscribed in a circle, the central angles subtended by each side are equal. The sum of the central angles of a circle is 360°. For a pentagon, the number of sides \(n = 5\).

Step2: Calculate the measure of each arc

The measure of each arc of a circle subtended by the sides of a regular pentagon is given by \(\frac{360^{\circ}}{n}\), where \(n = 5\). So, \(\frac{360}{5}=72^{\circ}\). So \(m\overparen{JK}=m\overparen{KL}=m\overparen{LM}=m\overparen{MN}=m\overparen{NJ}=72^{\circ}\)

Answer:

\(m\overparen{JK}=m\overparen{KL}=m\overparen{LM}=m\overparen{MN}=m\overparen{NJ}=72^{\circ}\)