The sum of all six exterior angles of triangle is ___________.
180
360
720
90
A
180
B
360
C
720
D
90
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Solution
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Here, we have six exterior angles namely ∠ABE,∠ACD,∠BAF,∠BCG,∠CAH,∠CBI. According to exterior angle theorem, m∠ACD=m∠A+m∠B m∠ABE=m∠A+m∠C m∠BAF=m∠B+m∠C m∠BCG=m∠A+m∠B m∠CAH=m∠B+m∠C m∠CBI=m∠A+m∠C Now, taking the sum of all the exterior angles of △ABC, we get m∠ACD+m∠ABE+m∠BAF+m∠BCG+m∠CAH+m∠CBI =4(m∠A+m∠B+m∠C) =4(180) =720.
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