An angle has a measure of 72^\circ. What is the measure of this angle in radians? — SAT

An angle has a measure of $72^\circ$ . What is the measure of this angle in radians?

The correct answer is

\frac{2\pi}{5}

radians.

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

\frac{\pi}{180}

. Doing so for

72^\circ

yields

\frac{72\pi}{180}

. Dividing the numerator and denominator by their greatest common divisor, 36, simplifies the fraction to

\frac{2\pi}{5}

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

\frac{\pi}{180}

\theta = 72 \times \frac{\pi}{180} = \frac{72\pi}{180}

The conversion factor from degrees to radians is

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

Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, 36.

\frac{72 \div 36}{180 \div 36}\pi = \frac{2\pi}{5}

Simplifying the fraction expresses the angle in standard reduced radian form.

Converting degrees to radians

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