In triangle ABC, BD is perpendicular to AC and CE is perpendicular to AB. If BD and CE intersect at O, prove that angle BOC =180-A
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Step-by-step explanation:
BD⊥AC
Hence, ∠BDA=90
o
CE⊥AB
Hence,∠CEA=90
o
In quadrilateral, AEID
∠A+∠AEI+∠AIE+∠IDA=360
o
∠A+90+∠EID+90=360
o
∠A+∠EID=180
o
∠EID=∠BIC (Vertically opposite angles)
∠A+∠BIC=180
o
∠BIC=180o −∠A
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