Question

observa el △jkl.
¿cuál es la medida del ∠k en radianes?
a. $\frac{5\pi}{12}$
b. $\frac{\pi}{3}$
c. $\frac{\pi}{4}$
d. $\frac{\pi}{6}$

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\) (or \(\pi\) radians). So, \(\angle J + \angle L + \angle K = 180^\circ\).

Step2: Substitute known angles

We know \(\angle J = 60^\circ\) and \(\angle L = 45^\circ\). Let \(\angle K = x\). Then \(60^\circ + 45^\circ + x = 180^\circ\).

Step3: Solve for \(x\)

\(x = 180^\circ - 60^\circ - 45^\circ = 75^\circ\).

Step4: Convert degrees to radians

To convert degrees to radians, use the formula \( \text{radians} = \text{degrees} \times \frac{\pi}{180} \). So, \(75^\circ \times \frac{\pi}{180} = \frac{75\pi}{180} = \frac{5\pi}{12}\).

Answer:

A. \(\frac{5\pi}{12}\)