Question

minor arc kl measures 135°. which is the radian measure of central angle kol? × \\(\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: \( \text{radians} = \text{degrees} \times \frac{\pi}{180^\circ} \).

Step2: Substitute the given degree measure

The central angle \( \angle KOL \) has a degree measure of \( 135^\circ \). Substitute into the formula: \( 135^\circ \times \frac{\pi}{180^\circ} \).

Step3: Simplify the expression

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 with \( \frac{3\pi}{4} \) radians)