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The figure shows three exterior angles of triangle ABC. Show that the measure of angle 1 plus the measure of angle 2 plus the measure of angle 3 equals 360​

The figure shows three exterior angles of triangle ABC Show that the measure of angle 1 plus the measure of angle 2 plus the measure of angle 3 equals 360 class=

Respuesta :

Step-by-step explanation:

Let the angle near point A be [tex]A[/tex].

Let the angle near point B be [tex]B[/tex].

Let the angle near point C be [tex]C[/tex].

Let the external angle near point A be [tex]extA[/tex].

Let the external angle near point B be [tex]extB[/tex].

Let the external angle near point C be [tex]extC[/tex].

According to exterior angle property,exterior angle of an angle is the sum of other two angles.

So,

[tex]extA=B+C\\extB=A+C\\extC=A+B[/tex]

According to angle sum property,the sum of angles in the triangle add to [tex]180[/tex]

[tex]extA+extB+extC=B+C+A+C+A+B=2(A+B+C)=2\times 180=360^{0}[/tex]

Answer:

The correct answer is A on Edge 2021

Step-by-step explanation: