Question

Prove that angle boc =180-angle A

Answer 1

Given that ΔABC, BD⊥ AC and CE ⊥ AB.

To prove ∠BOC = 180° - ∠A.

Proof :
Given BD⊥ AC

∴ ∠BDA = 90°.

Given CE ⊥ AB

∴ ∠CEA = 90°

In Quadrilateral AEOD

∠A + ∠AEO + ∠EOD + ∠ADO = 360°

∠A + 90° + ∠EOD + 90° = 360°


∠A + ∠EOD  = 360° - 180° = 180°

Since ∠EOD = ∠BOC  ( vertically opposite angles)

∠A + ∠BOC = 180°

∠BOC = 180° - ∠A.

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