Question

in the figure below, m∠ jsr = 57° and m∠ sln = 79°.
note: picture not drawn to scale
what is m∠ lns?
a. 22°
b. 44°
c. 66°
d. 136°

Explanation:

Step1: Identify Vertical Angles

$\angle JSR$ and $\angle LSN$ are vertical angles, so $m\angle LSN = m\angle JSR = 57^\circ$.

Step2: Use Triangle Angle Sum

In $\triangle SLN$, the sum of angles is $180^\circ$. We know $m\angle SLN = 79^\circ$ and $m\angle LSN = 57^\circ$. Let $m\angle LNS = x$. Then $x + 57^\circ + 79^\circ = 180^\circ$.

Step3: Solve for x

$x = 180^\circ - 57^\circ - 79^\circ = 44^\circ$.

Answer:

B. $44^\circ$