Question -
Answer -
Given : In ∆ABC, sides AB and AC are produced to D and E respectively. Bisectors of interior ∠B and ∠C meet at P and bisectors of exterior angles B and C meet at Q.
To prove : ∠BPC + ∠BQC = 180°
Proof : ∵ PB and PC are the internal bisectors of ∠B and ∠C
∠BPC = 90°+ 
∠A …(i) Similarly, QB and QC are the bisectors of exterior angles B and C
∴ ∠BQC = 90° + ∠A …(ii) Adding (i) and (ii),
∠BPC + ∠BQC = 90° + ∠A + 90° – ∠A = 90° + 90° = 180°
Hence ∠BPC + ∠BQC = 180°