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

Step2: Substitute the given degree measure

We are given the central angle (since it's a central angle, its measure is equal to the measure of the minor arc KL) as \( 135^\circ \). Substitute \( 135 \) into the formula: \( 135 \times \frac{\pi}{180} \).

Step3: Simplify the fraction

Simplify \( \frac{135}{180} \). Both numerator and denominator are divisible by 45. \( 135 \div 45 = 3 \) and \( 180 \div 45 = 4 \). So we get \( \frac{3\pi}{4} \).

Answer:

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