Question

A lamp weighs 182N. It's supported by 2 wires that are 110 deg between each. What is the tension

Answer 1

The geometry is symmetric, with the wires forming a V with 110o the apex angle. Thus, the angle of the wire versus horizontal is 90-55=35o.
Each wire contributes half the support. Taking wire 2 on the right side, we have T2 sin(35) = 91 N. This makes T2=111 N, and T1 = 111 N, also.
Check: moving the wires together gives sin(90)=1 and T1=T2=91 N each. Note that the more nearly horizontal the wires, sin(small) gets small and the tension gets very high.

Answer 2

T1, T2 should be 158.65N

Answer 3

If the picture is drawn like this, I agree with @alekos 's answer