Answer:
Option B.
Step-by-step explanation:
Given information: JM ⊥ NK, [tex]\widehat{MN}=55^{\circ}[/tex].
According to the angle inside the circle theorem, if two chords intersect each other internally then the resultant intercepted angle is equal to the half of the sum of intercepted arc.
Using the angle inside the circle theorem, we get
[tex]\angle JLK=\frac{1}{2}(\widehat{MN}+\widehat{JK})[/tex]
[tex]90^{\circ}=\frac{1}{2}(55^{\circ}+\widehat{JK})[/tex]
Multiply both sides by 2.
[tex]180^{\circ}=55^{\circ}+\widehat{JK}[/tex]
Subtract both sides by 55.
[tex]180^{\circ}-55^{\circ}=55^{\circ}+\widehat{JK}-55^{\circ}[/tex]
[tex]125^{\circ}=\widehat{JK}[/tex]
The measure of arc JK is [tex]125^{\circ}[/tex].
Therefore, the correct option is B.
