A wheel rotates through a central angle of \frac{11\pi}{18} radians. What is the measure o… — SAT

A wheel rotates through a central angle of $\frac{11\pi}{18}$ radians. What is the measure of this angle in degrees?

Answer: 110 degrees

110

To convert radians to degrees, multiply the angle by

\frac{180}{\pi}

. Thus,

\frac{11\pi}{18} \times \frac{180}{\pi} = 110

. The measure of the angle is 110 degrees.

Identify the conversion relationship between radians and degrees.

Multiply the angle in radians by

\frac{180}{\pi}

to convert to degrees.

Since

\pi

radians is equal to

180

degrees, the conversion factor is

\frac{180}{\pi}

Multiply the given radian measure of

\frac{11\pi}{18}

by the conversion factor.

110

Applying the conversion factor simplifies the expression by canceling

\pi

and dividing

180

18

to get

10

, which is then multiplied by

11

to get the final degree measure.

To convert an angle from radians to degrees, multiply the angle in radians by

\frac{180}{\pi}

Estimated Time:45s

Question