Question

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

• A. $180$
• B. $360$
• C. $720$
• D. $90$

Answer 1

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 $△ABC$, we get
$m\angle ACD+m\angle ABE+m\angle BAF+m\angle BCG+m\angle CAH+m\angle CBI$
$=4(m\angle A+m\angle B+m\angle C)$
$=4\left(180\right)$
$=720$.