In ΔABC, AB and AC are produced to points D and E, respectively. If the bisectors of ∠CBD and ∠BCE meet at point O such that ∠BOC=76
∘
, then ∠A= ?

The point O is the ex-centre of the triangle formed by external angle bisectors.
The relationship between ∠BOC and ∠A is given by:

∠BOC=90
∘
−
2
∠A
​

Given ∠BOC=76
∘
:

76
∘
=90
∘
−
2
∠A
​

2
∠A
​
=90
∘
−76
∘

2
∠A
​
=14
∘

∠A=28
∘