Answer:
Option B.
Step-by-step explanation:
Given information: [tex]m\angle A=48^{\circ},\angle E=90^{\circ},\angle EMS=59^{\circ}[/tex].
According to the angle sum property of a triangles, the sum of interior angles of a triangle is 180°.
Apply angle sum property on triangle AEJ.
[tex]\angle A+\angle E+\angle J=180^{\circ}[/tex]
[tex]48^{\circ}+90^{\circ}+\angle J=180^{\circ}[/tex]
[tex]138^{\circ}+\angle J=180^{\circ}[/tex]
Subtract 138 from both sides.
[tex]\angle J=180^{\circ}-138^{\circ}[/tex]
[tex]\angle J=42^{\circ}[/tex]
The measure of angle J is 42°.
According to exterior angle property, the sum of two interior angles of a triangle is equal to the third exterior angle.
Apply exterior angle property on triangle JMS.
[tex]\angle EJA+\angle JSM=\angle EMS[/tex]
[tex]42^{\circ}+\angle JSM=59^{\circ}[/tex]
Subtract 42 from both sides.
[tex]\angle JSM=59^{\circ}-42^{\circ}[/tex]
[tex]\angle JSM=17^{\circ}[/tex]
The measure of ∠JSM is 17°.
Therefore, the correct option is B.
