If you has asked about "Agriculture is one of the most importants segments of the economy" I would have given an unqualified yes.
"Industry" often refers to big plants that build things. So if you are referring to building tractors and havesters and other farm equipment, then "Agriculture [products] is a branch of industry" would be okay too.
But if you are referring to farming and raising animals and crops, then I would not say it's a branch of industry. It's (in my opinion) as segment of the overall economy.
[writer, not teacher]