Question

in the figure below, m∠jsr = 57° and m∠sln = 79°. what is m∠lns? a. 44° b. 66° c. 22° d. 136°

Explanation:

Step1: Recall the property of angles in a triangle

The sum of interior angles of a triangle is 180°. In \(\triangle SLN\), we know \(\angle SLN = 79^{\circ}\), and we assume \(\angle LSN\) and \(\angle LNS\) are the other two - angles. Also, \(\angle JSR\) and \(\angle LSN\) are vertical angles.
Since vertical angles are equal, \(\angle LSN=\angle JSR = 57^{\circ}\).

Step2: Calculate \(\angle LNS\)

Let \(\angle LNS=x\). Using the angle - sum property of a triangle (\(\angle SLN+\angle LSN+\angle LNS = 180^{\circ}\)), we substitute the known values: \(79^{\circ}+57^{\circ}+x = 180^{\circ}\).
First, add the known angles on the left - hand side: \(79 + 57=136\). So the equation becomes \(136^{\circ}+x = 180^{\circ}\).
Then, solve for \(x\): \(x=180^{\circ}-136^{\circ}=44^{\circ}\).

Answer:

A. \(44^{\circ}\)