To solve for [tex]\( x \)[/tex], let's analyze the given information:
1. [tex]\( W \)[/tex] bisects [tex]\( \angle XWY \)[/tex]. This means that [tex]\( \angle XWW \)[/tex] and [tex]\( \angle VWY \)[/tex] are equal since [tex]\( W \)[/tex] is the bisector of [tex]\( \angle XWY \)[/tex].
2. The measure of [tex]\( \angle XWW \)[/tex] is given as [tex]\( (x + 3) \)[/tex].
3. The measure of [tex]\( \angle VWY \)[/tex] is given as [tex]\( (3x - 91) \)[/tex].
Since [tex]\( W \)[/tex] bisects [tex]\( \angle XWY \)[/tex], we set the two expressions for the angles equal to each other:
[tex]\[
x + 3 = 3x - 91
\][/tex]
Now, solve for [tex]\( x \)[/tex]:
1. Subtract [tex]\( x \)[/tex] from both sides to start isolating [tex]\( x \)[/tex]:
[tex]\[
3 = 3x - x - 91
\][/tex]
[tex]\[
3 = 2x - 91
\][/tex]
2. Add 91 to both sides to continue isolating [tex]\( x \)[/tex]:
[tex]\[
3 + 91 = 2x
\][/tex]
[tex]\[
94 = 2x
\][/tex]
3. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{94}{2}
\][/tex]
[tex]\[
x = 47
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{47}
\][/tex]
The correct choice is C.
