AB is a diameter of a circle. C and D are points on the opposite sides of the diameter AB, such that ∠ACD = 25°. E is a point on the minor arc BD. Find the measure of ∠BED (in degrees).

Since AB is a diameter, ∠ACB = 90° (angle in a semicircle). Given ∠ACD = 25°, the minor arc BD measures 2 × 90° + 2 × 25° = 230° (the arc subtended by the diameter plus the angle). Angle ∠BED is an inscribed angle subtending arc BD, so it equals half the measure of arc BD: ∠BED = 230°/2 = 115°. Alternatively, note that points A, C, D, B are concyclic with opposite angles summing to 180°.