A circle has a radius of 5 in. A central angle that measures 150° cuts off an arc.
Explain how to find the arc length exactly, and then approximate it to one decimal place.

Part 1) The exact value of the arc length is \frac{25}{6}\pi \ in

Part 2) The approximate value of the arc length is 13.1\ in

Step-by-step explanation:

ind the circumference of the circle

The circumference of a circle is equal to

C=2\pi r

we have

r=5\ in

substitute

C=2\pi (5)

C=10\pi\ in

step 2

Find the exact value of the arc length by a central angle of 150 degrees

Remember that the circumference of a circle subtends a central angle of 360 degrees

by proportion

\frac{10\pi}{360} =\frac{x}{150}\\ \\x=10\pi *150/360\\ \\x=\frac{25}{6}\pi \ in

Find the approximate value of the arc length

To find the approximate value, assume

\pi =3.14

substitute

\frac{25}{6}(3.14)=13.1\ in

answer with step-by-step explanation:

a. ∠j is supplementary to ∠k - true:

(opposite angles of a trapezoid are supplementary which means that they add up to 180 degrees)

b. kl is parallel to jm - true:

(opposite sides are parallel to each other in a trapezoid)

c. jk is perpendicular to kl - false:

(clearly, jk does not make a right angle with kl)

d. jk is parallel to lm - false:

(jk and lm are two lines opposite in direction to each other so they cannot be parallel)

e. ∠j is congruent to ∠m - true:

(the angles on each side of the base are congruent)

f. ∠j is congruent to ∠k - false:

(the angles on the same side but opposite side of the base are not congruent)

2

step-by-step explanation: