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The supplement of an angle is 180° - angle. Here, the supplement of the angle is 155°, so the original angle must be 180° - 155° = 25°.
The complement of an angle is 90° - angle. Since the original angle is 25°, the complement of the angle is 90° - 25° = 65°.
Therefore, the measure of the complement of the angle is 65°, which corresponds to option B.