Final answer:
The measure of arc BC⎯ in the circle is 130 degrees, as it is twice the measure of the inscribed angle ∠BDC of 65 degrees.
Step-by-step explanation:
The measure of ⎯BC in a circle with an inscribed angle ∠BDC of 65 degrees can be calculated using the fact that the measure of the arc is twice the measure of the inscribed angle. An inscribed angle is formed by two chords in a circle (in this case BD and DC) that intersect on the circumference of the circle. The arc ⎯BC, which is the part of the circle's circumference between points B and C and lies in the interior of ∠BDC, will have a measure of 2 × 65° = 130°.