With questions involving Forces, it is best to draw a force diagram to model the problem, like the one shown below
We have two tension acting on the particle; T₁ and T₂. The tensions are vectors directed toward the ceiling.
There's also the force as weight acting vertically downwards from the particle. This force is 150N.
As the tension force acting in an angle, we will have to consider the sine and sine components of the tensions.
We will also solve the force in the direction of x-axis and y-axis
Solving in x-axis direction:
T₂ cos 40° - T₁ cos 40° = 0
T₂ cos 40° = T₁ cos 40°
T₂ = T₁ ...(Eq 1)
Solving in y-axis direction:
T₁ sin 40° + T₂ sin 40° - 150N = 0
T₁ sin 40° + T₂ sin 40° = 150 ⇒ we know from (Eq 1) that T₁ = T₂
2T₁ sin 40° = 150
T₁ sin 40° = 75
T₁ = 75 ÷ sin 40°
T₁ = 116.7 N
Since T₁ = T₂, so T₂ = 116.7N