Question

minor arc kl measures 135°. which is the radian measure of central angle kol? options: \\( \frac{3\pi}{8} \\) radians, \\( \frac{3\pi}{4} \\) radians, \\( \frac{7\pi}{8} \\) radians, \\( \frac{13\pi}{5} \\) radians

Explanation:

Step1: Recall degree to radian formula

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

Step2: Substitute the given degree measure

The central angle \( \angle KOL \) has a measure equal to the minor arc \( KL \), which is \( 135^\circ \). Substitute \( 135^\circ \) into the formula:
\( 135 \times \frac{\pi}{180} \)

Step3: Simplify the fraction

Simplify \( \frac{135}{180} \). Both numerator and denominator are divisible by 45: \( \frac{135 \div 45}{180 \div 45} = \frac{3}{4} \). So the radian measure is \( \frac{3\pi}{4} \) radians.

Answer:

\( \frac{3\pi}{4} \) radians (corresponding to the option: \( \boldsymbol{\frac{3\pi}{4}} \) radians)