The circumcentre of a triangle ABC is 'O'. If ∠BAC = 85° and ∠BCA = 75°, then the value of ∠OAC is -

Question: The circumcentre of a triangle ABC is 'O'. If ∠BAC = 85° and ∠BCA = 75°, then the value of ∠OAC is -

Solution:
According to the question,
Given:
∠BAC = 85°
∠BCA = 75°
∠OAC = ?


∠ABC + ∠BCA + ∠CAB = 180°
⇒ ∠ABC + 75° + 85° = 180°
∴ ∠ABC = 20°

∠COA = 2 × ∠ABC
⇒ ∠COA = 2 × 20 = 40°

In ΔAOC,
We know OC = OA
∴ ∠OAC = ∠OCA
∴ ∠OAC + ∠OCA + ∠COA = 180°
⇒ 2∠OAC = 180° - 40°
⇒ 2∠OAC = 140°
∴ ∠OAC = 70°