Final answer:
By applying circle geometry rules, the angle formed by two intersecting chords is calculated as half the sum of the intercepted arcs. The value of x is found through algebraic manipulation, giving a result of 7.65.
Step-by-step explanation:
The student has asked a question involving circle geometry and algebra. In circle C with chords WV and XY, the measure of arc XY is given as 104°. If the measure of angle VWX (m∠VW) is expressed as 23x+4, we need to find the value of x. Since WX and VY are chords intersecting inside the circle, the angle formed by these two chords is equal to half the sum of the measures of the arcs they intercept, which are arc XY and opposite arc WV. Therefore, m∠VW = (arc XY + arc WV) / 2.
We are given that arc XY is 104°. The entire circle has 360°, so arc WV is 360° - 104° = 256°. Therefore, m∠VW = (104° + 256°) / 2 = 180°. Now we can set up our equation: 23x + 4 = 180. Subtracting 4 from both sides, we get 23x = 176. Dividing both sides by 23 gives us x = 176 / 23, which simplifies to x = 7.65. However, since we expect an integer answer as per the multiple-choice options, it seems there is an error in the provided question or given choices. Therefore the exact value of x cannot be determined from the provided options.