If the measure of an angle is \frac{5\pi}{4} radians, what is its measure in degrees? — SAT

If the measure of an angle is $\frac{5\pi}{4}$ radians, what is its measure in degrees?

225^\circ

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

\frac{180^\circ}{\pi}

. Multiplying

\frac{5\pi}{4}

\frac{180^\circ}{\pi}

simplifies to

\frac{5}{4} \times 180^\circ = 5 \times 45^\circ = 225^\circ

. Therefore, the correct degree measure of the angle is

225^\circ

Set up the conversion from radians to degrees by multiplying the given radian measure by

\frac{180^\circ}{\pi}

\frac{5\pi}{4} \times \frac{180^\circ}{\pi}

Since

\pi

radians is equal to

180^\circ

, multiplying by the conversion factor

\frac{180^\circ}{\pi}

converts the units from radians to degrees.

Simplify the expression by canceling the

\pi

terms and performing the arithmetic.

225^\circ

The

\pi

in the numerator and denominator cancel out, leaving

\frac{5}{4} \times 180^\circ

. Dividing

180

4

gives

45

, and multiplying

5

45

yields

225

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

\frac{180^\circ}{\pi}

Another way to convert is to substitute

180^\circ

directly for

\pi

in the expression:

\frac{5\pi}{4} = \frac{5(180^\circ)}{4} = 5 \times 45^\circ = 225^\circ

Tahmini Süre:45s

Soru