The sides AB and AC of △ABC are produced to points D and E, respectively. The bisectors of ∠CBD and ∠BCE meet at P. If ∠A=72
∘
, then the measure of ∠P is:

The point P is the ex-center of △ABC formed by the exterior angle bisectors at vertices B and C.
The standard formula for the angle formed by exterior angle bisectors is:

∠P=90
∘
−
2
∠A
​

Given ∠A=72
∘
:

∠P=90
∘
−
2
72
∘

​

∠P=90
∘
−36
∘
=54
∘