Does Wang Mang belong to Wang Langya?

No, Wang Mang is the Tian family of Qi State, a descendant of Qi State.

According to the Records of Later Han Dynasty and Dialectics of Ancient and Modern Surnames, Tian 'an was once named King of Northern Hebei by Xiang Yu, Liu Bang founded the Han Dynasty, and Tian 'an lost his country. Because he is the king of Qi, people in Qi call his family "Wang", so he takes "Wang" as his surname. For example, King Qingzhou and King Chen Liu (now Kaifeng, Henan Province) all came from Tianan, and they are the most descendants of these kings.