From the given circle,
X is the center of the circle
The arc intercepted by two radii is equal to the angle formed by the two radii a the center of the circle. This means that
arc SW = angle SXW
Thus, angle SXW = 72 degrees
Again,
angle SXW and angle UXV are vertically opposite angles. Verticall opposite angles are equal. This means that
angle SXW = angle UXV
angle UXV = 72 degrees
Also,
angle WXV and angle SXU are vertically opposite angles. This means that
angle WXV = angle SXU
Recall, the sum of the angles in a circle is 360 degrees. This means that
angle SXU + angle WXV + angle SXW + angle UXV = 360
Since angle WXV = angle SXU, then
angle SXU + angle SXU + 72 + 72 = 360
2angle SXU + 144 = 360
2angle SXU = 360 - 144 = 216
angle SXU = 216/2 = 108
Thus,
angle VXW = 108 degrees
Referring to the first theorem that we applied,
arc WV = 108 degrees
arc TU = 87 degrees
arc TVW = 87 + 72 + 108
arc TVW = 267 degrees
arc ST + arc TU = arc STU
By applying the first theorem,
arc STU = angle SXU
arc STU = 108
Thus,
arc ST + 87 = 108
arc ST = 108 - 87
arc ST = 21 degrees