The correct option is option D: the measure of WX is 32°.
What is central angle theorem?
The central angle theorem states that the central angle of an arc on the circle is always twice the inscribed angle from those end two points of the arc.
Here in the figure, Connect X to T
Let the center of the circle is O.
∠TSX=41°
The measure of the arc TR is 114°.
∠TOR=114°
So by the central angle theorem, the central angle of an arc is twice of any circumference angle on the circle.
∠TOR=2∠TXR
⇒114°=2∠TXR
⇒∠TXR=114°/2
⇒∠TXR=57°
As we know the external angle of the triangle is the sum of the two farthest internal angels of the triangle.
In triangle ΔTXR,
∠TXR=∠STX+∠TSX
⇒57°=∠STX+41°
⇒∠STX=57°-41°
⇒∠STX=16°
⇒∠WTX=16°
So, using by central angle theorem, the central angle of an arc is twice of any circumference angle on the circle.
for arc WX,
∠WOX=2∠WTX
⇒∠WOX= 2*16°
⇒∠WOX=32°
Therefore the measure of WX is 32°.
Learn more about the central angle theorem
here: https://brainly.com/question/27203912
#SPJ2
