To find the measure of angle \( \angle B \) formed by the tangent segments from point \( B \) to points \( C \) and \( D \) on the circle, we can use the following theorem:
The measure of the angle formed by two tangent segments drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs.
In this case, since point \( B \) lies outside the circle and the arcs intercepted by the tangents are \( \overarc{CD} \) and the remainder of the circle, the angle \( \angle B \) can be determined by the formula:
\[ \angle B = \frac{1}{2} \left( \text{measure of arc } CD - \text{measure of arc } AB \right) \]
Since \( CD \) is given as \( 73^\circ \), and assuming that the remainder of the circle (the arc not covered by \( CD \)) completes the entire circle, the other arc \( AB \) can be calculated as:
\[ \text{measure of arc } AB = 360^\circ - \text{measure of arc } CD = 360^\circ - 73^\circ = 287^\circ \]
Now we can substitute these values into the formula:
\[ \angle B = \frac{1}{2} \left( 287^\circ - 73^\circ \right) = \frac{1}{2} \left( 214^\circ \right) = 107^\circ \]
Thus, the measure of \( \angle B \) is \( 107^\circ \).