Answer:
Step-by-step explanation:
Given:
On the outside of the circle, we have points T, V, and U.
Inside the circle, there is point W.
The central angles are as follows:
(m \angle TWV = 13x - 36^\circ)
(m \angle VWU = 4x + 93^\circ)
(m \angle UWT = 8x - 47^\circ)
We know that the sum of the central angles around a point (in this case, point W) is (360^\circ). Therefore: [m \angle TWV + m \angle VWU + m \angle UWT = 360^\circ]
Substitute the given expressions for the angles: [13x - 36 + 4x + 93 + 8x - 47 = 360]
Combine like terms: [25x + 10 = 360] [25x = 350] [x = 14]
Now let’s find (m \angle VWU): [m \angle VWU = 4x + 93 = 4(14) + 93 = 149^\circ]
Therefore, the measure of angle (m \angle UWV) is 149 degrees.