In △ABC, the internal angle bisectors of ∠B and ∠C meet at O (the incenter). If ∠A = 70°, find ∠BOC.

Introduction / Context:The incenter is the intersection of the internal angle bisectors. A standard identity links ∠BOC at the incenter with the opposite vertex angle ∠A of the triangle.

Given Data / Assumptions:O is the incenter; A = 70°.

Concept / Approach:For the incenter, the angle between lines OB and OC equals 90° + (A/2). This comes from the tangency geometry of the incircle and angle-bisector properties.

Step-by-Step Solution:

Verification / Alternative check:Test with a sample triangle (e.g., A=70°, B=60°, C=50°). Construct bisectors and measure angle at the incenter; it matches 125° per the identity.

Why Other Options Are Wrong:135°, 115°, 110° correspond to misapplied formulas (e.g., 90° ± A/2) or rounding errors; only 125° fits the incenter rule.

Common Pitfalls:Confusing excenter and incenter results: excenter would use 90° − A/2 for the angle between external bisectors at B and C.

Final Answer:125°