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Question

The sum of all six exterior angles of triangle is ___________.


A
180
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B
360
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C
720
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D
90
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Solution

The correct option is C $$720$$
Here, we have six exterior angles namely $$\angle ABE, \angle ACD, \angle BAF, \angle BCG, \angle CAH, \angle CBI$$.
According to exterior angle theorem,
$$m\angle ACD = m\angle A + m\angle B$$
$$m\angle ABE = m\angle A + m \angle C$$
$$m\angle BAF = m\angle B + m\angle C$$
$$m \angle BCG = m\angle A + m\angle B$$
$$m \angle CAH = m\angle B + m\angle C$$
$$m \angle CBI = m \angle A + m \angle C$$
Now, taking the sum of all the exterior angles of $$\triangle ABC$$, we get
$$m \angle ACD + m \angle ABE + m \angle BAF + m \angle BCG + m \angle CAH + m \angle CBI$$
$$= 4(m \angle A + m \angle B + m \angle C)$$
$$= 4(180)$$
$$= 720$$.
736087_715012_ans_60d5e1887ec245ec87fbc00514d4b7a3.jpg

Mathematics

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