In the second diagram, we are given that angle EDF = 58 degrees. E and F are points on the circle, and D is a point outside the circle. DE and DF are secant lines or tangents. The diagram shows that DE and DF are tangent to the circle at points E and F respectively. The red cross is near point R, which is on the circle. The angle EDF is the angle between the two tangents from point D to the circle. There is a theorem that states that the angle formed by two tangents drawn from an external point to a circle is equal to half the difference between the measures of the intercepted arcs. Let the intercepted arcs be arc EF (minor) and arc E_major_F (major). Then, angle EDF = 1/2 * (measure of major arc EF - measure of minor arc EF). We know that the sum of the measures of the major and minor arcs is 360 degrees. Let the measure of the minor arc EF be x. Then the measure of the major arc EF is 360 - x. So, 58 = 1/2 * ((360 - x) - x). 58 = 1/2 * (360 - 2x). 116 = 360 - 2x. 2x = 360 - 116. 2x = 244. x = 122 degrees. So, the measure of the minor arc EF is 122 degrees. The red cross near R is unexplained and seems irrelevant to finding the measure of arc EF or any angles related to EDF. If R is a point on the major arc EF, then the angle subtended by the minor arc EF at R (angle ERF) would be half the measure of the minor arc EF. So, angle ERF = 122 / 2 = 61 degrees. If R is on the minor arc EF, then angle ERF would subtend the major arc EF, and angle ERF = (360-122)/2 = 238/2 = 119 degrees. However, angles in a triangle are usually less than 180 degrees, so R is likely on the major arc. The question is implicitly asking for what can be deduced. We can find the measure of the minor arc EF. Let's assume R is a point on the major arc EF. The angle subtended by the minor arc EF at the circumference is angle ERF = (1/2) * arc EF. The angle formed by two tangents from an external point D is given by angle EDF = 58 degrees. The theorem states that angle EDF = 1/2 * (measure of major arc EF - measure of minor arc EF). Let the measure of minor arc EF be x. Then the measure of major arc EF is 360 - x. So, 58 = 1/2 * ((360 - x) - x). 58 = 1/2 * (360 - 2x). 116 = 360 - 2x. 2x = 360 - 116. 2x = 244. x = 122 degrees. So, the measure of the minor arc EF is 122 degrees. The red cross near R is not used.