Given:
Consider the below figure attached with this question.
In Circle Y, Chords R T and S U intersect.
Arc RS is 106 degrees.
The angle that intercepts arc RS is 94 degrees.
To find:
The measure of arc(TU).
Solution:
If two chords intersect each other insider the circle, then the half of sum of intercepted arcs is equal to the angle on intersection of those arcs.
For the given problem,
[tex]\dfrac{1}{2}[m(arc RS)+m(arc TU)]=94^\circ[/tex]
[tex]\dfrac{1}{2}[106^\circ+m(arc TU)]=94^\circ[/tex]
[tex]106^\circ+m(arc TU)=2\times 94^\circ[/tex]
[tex]106^\circ+m(arc TU)=188^\circ[/tex]
[tex]m(arc TU)=188^\circ-106^\circ[/tex]
[tex]m(arc TU)=82^\circ[/tex]
The measure of arc(TU) is 82 degrees.
Therefore, the correct option is A.
