Answer
C. DC
Step-by-step explanation
AB = BC.
From the diagram, <DAB = <DBC = 60°
<ADB = 180 - (60 + 60)
= 180 - 120
= 60°
But we have been given angle BDC = 37.5°.
Since the angle BDC is smaller than ADN, the line AD is smaller than DC. AB = AD since triangle ABD is an equilateral triangle.
∴ The longest segment shown is DC.