Induction motor electrical and mechanical angle
How do we reach the relation between mechanical angle(θm) and
  electrical angle(\$θ_e\$) as: \$θ_e\$=(P/2)\$θ_m\$ ? ; where P is the number of
  poles.


An electrical machine is simply an electrical&lt;>mechanical energy conversion device which utilises magnetic fields as the exchange medium.

When an electrical machine is operating as a motor, the idea is to create a traveling, rotating magnetic field, via the stator and "hope" 1 that this moving flux attracts the rotor (be it via an equivalent magnetic field or via an affinity to reduce the reluctance)  

So a stator:



A 3 phase, single pole pair topology. If the stator was now unrolled



you can now see that for 360degree electrical we have equally achieved 360degree mechanical.

As the number of pole-pairs is increased, the point at which an electrical cycle is completed becomes a fraction of the main mechanical cycle &amp; this factor is the pole-pair count 

1 hope is used because there are some prerequisites that must be met that are machine specific. freq, voltage, load, supply ...