Given:
NR = 10 m
Measure of arc MQ = 162 degrees
Let's find the length of arc NP.
Here, we have:
Measure of arc MQ = Measure of arc NP
Now apply the Angle-arc relationship, we have:
Measure of arc NP = measure of angle NRP = 162 degrees.
To find the length of arc NP, apply the formula;
[tex]arc_{NP}=\frac{\theta}{360}*2\pi r[/tex]
Where:
θ = 162 degrees
r is the radius = NR = 10 m
Thus, we have:
[tex]\begin{gathered} arc_{NP}=\frac{162}{360}*2\pi *10 \\ \\ arc_{NP}=0.45*62.83 \\ \\ arc_{NP}=28.27\text{ m} \end{gathered}[/tex]
Therefore, the length of arc NP is 28.27 m.
ANSWER:
28.27 m
