Count the electron pairs around the central atom

The central atom has:

• 3 single bonds $\Rightarrow 3$ bond pairs
• 2 lone pairs $\Rightarrow 2$ lone pairs

So, total electron pairs around the central atom: $3 + 2 = 5$

Determine the electron-pair geometry

For 5 electron pairs, according to VSEPR theory, the electron-pair geometry is: $\text{Trigonal bipyramidal}$

Place the lone pairs in the most stable positions

In a trigonal bipyramidal arrangement, lone pairs prefer equatorial positions because these positions have fewer $90^\circ$ interactions.

Since there are 2 lone pairs, both occupy equatorial positions.

Find the molecular shape

After placing 2 lone pairs equatorially, the 3 bonded atoms occupy:

• 2 axial positions
• 1 equatorial position

This gives the molecular shape: $\text{T-shaped}$

Check the options

• A: trigonal pyramidal $\rightarrow$ corresponds to $AX_3E$, not correct
• B: T-shaped $\rightarrow$ corresponds to $AX_3E_2$, correct
• C: see-saw $\rightarrow$ corresponds to $AX_4E$, not correct
• D: planar triangular $\rightarrow$ corresponds to $AX_3$, not correct

Final answer

The molecule has the type: $AX_3E_2$ Hence its shape is: $\boxed{\text{T-shaped}}$