Question

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

Answer 1

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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