Question

complete the proportion to find the arc length of the minor arc \\(pq\\).

what is the measure of the central angle for the minor arc, \\(pq\\)? \\(^{\circ}\\)

\\(\frac{ }{360^{\circ}} = \frac{x}{2\pi( )}\\)

find the arc length of \\(pq\\). write your answers using pi with no spaces.

\\(\text{length}_{\text{arc}} = \\) units

Explanation:

Find the central angle of the minor arc

$$ \theta = 360^\circ - 210^\circ = 150^\circ $$

Set up the arc length proportion

$$ \frac{150^\circ}{360^\circ} = \frac{x}{2\pi(30)} $$

Solve for the arc length

$$ x = \frac{150}{360} \cdot 60\pi = \frac{5}{12} \cdot 60\pi = 25\pi $$

Answer:

Question 1

What is the measure of the central angle for the minor arc, \(\widehat{PQ}\)? <blank>150</blank>\(^\circ\)

Question 2

Complete the proportion to find the arc length of the minor arc \(\widehat{PQ}\):
\(\frac{\text{<blank>150</blank>}}{360^\circ} = \frac{x}{2\pi(\text{<blank>30</blank>})}\)

Question 3

Find the arc length of \(\widehat{PQ}\). Write your answers using 'pi' with no spaces.
\(\text{Length}_{\widehat{PQ}} =\) <blank>25pi</blank> units