Question

The sum of all exterior angles of a triangle is

• A. ${180}^{\circ }$
• B. ${360}^{\circ }$
• C. ${540}^{\circ }$
• D. ${720}^{\circ }$

Answer 1

The correct option is B

${360}^{\circ }$

Explanation for the correct answer:

Option(B):${360}^{\circ }$

In the above figure below, $1,2$ and $3$ are the interior angles whereas $4,5$ and $6$ are exterior angles. Using linear pair axiom, we can say that:

$1+4=180°$

$3+6=180°$

$2+5=180°$

Adding all of them, we get:

$(1+4)+(3+6)+(2+5)=540°$

Rearranging the terms, we get:

$(1+2+3)+(4+5+6)=540°$

$1+2+3=180°$(Angle Sum Property of a triangle)

So, $(4+5+6)=540°-180°=360°$

So, the sum of the exterior angles of a triangle is $360°$.

Hence, option(B) is the correct answer.

Explanation for the incorrect answer:

Option(A),Option(C) and Option(D):

By using the linear pair axiom, the sum of the exterior angles of a triangle we get $360°$.

So, options(A),(C) and (D) are incorrect answers.

Therefore, option(B) is the correct answer.