Question

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

Explanation:

Step1: Convert degrees to radians

To convert degrees to radians, use the formula \( \text{Radians}=\frac{\pi}{180}\times\text{Degrees}\).
Given the degree measure is \(135^{\circ}\), so \( \text{Radians}=\frac{\pi}{180}\times135\).

Step2: Simplify the expression

\(\frac{\pi}{180}\times135=\frac{135\pi}{180}\).
Simplify \(\frac{135\pi}{180}\) by dividing numerator and denominator by 45. \( \frac{135\div45}{180\div45}\pi=\frac{3\pi}{4}\).

Answer:

\(\frac{3\pi}{4}\text{ radians}\) (the second option in the given choices)