We need to find the measure of angle theta such that the circle is tangent to line vw.
For the circle to be a tangent circle, it will only touch the segment vw at one point. This condition is not met if the angle theta is different from 90°:
As you can see, when the angle is not 90°, the circle touches the segment at more than one point, which is not valid for a tangent circle.
Thus, the angle has to be equal to 90°:
Answer:
90°
