Question

what is ( mangle pqr ) in radians?
diagram: circle with center ( q ), points ( p ) and ( r ) on the circle, ( angle pqr = 63^circ )
options: (\frac{pi}{13}) radian, (\frac{11.340}{pi}) radians, (\frac{7pi}{20}) radians, (\frac{63pi}{3}) radians

Explanation:

Step1: Recall the conversion formula

To convert degrees to radians, we use the formula: \( \text{radians} = \text{degrees} \times \frac{\pi}{180} \).

Step2: Substitute the given degree measure

We are given the angle \( \angle PQR = 63^\circ \). Substituting into the formula:
\( 63 \times \frac{\pi}{180} \)

Step3: Simplify the fraction

Simplify \( \frac{63}{180} \). Both numerator and denominator are divisible by 9: \( \frac{63\div9}{180\div9} = \frac{7}{20} \). So the angle in radians is \( \frac{7\pi}{20} \).

Answer:

\( \frac{7\pi}{20} \) radians (corresponding to the option " \( \frac{7\pi}{20} \) radians")