Given the measure of the angle created by two tangent lines, it is possible to find the measure of the angle between the chord from their two points of tangency and one of the tangent lines. Remember that two tangent lines drawn from a point outside of a circle creates two congruent segments from that point to the points of tangency. As a result, these segments, along with the chord between their two points of tangency, create an isosceles triangle. Recall that an isosceles triangle has two congruent base angles. The sum of the angles in a triangle is 180°, so by subtracting the known angle created by the tangent lines, the remaining value is the measure of two times the base angle. Divide by 2 to find the measure of the desired angle.