Question

show that the sum of the exterior angles
of angle ABC is 360​

Answer 1

Step-by-step explanation:

Consider AABC in which ZA=1, 2B=2 and ZC Let the exterior angles of A, B and C be za, zb

= 3

and zc respectively.

Recall that sum of angles in a triangle is 180* That is 21+22+43 = 180°

From the figure, we have

21+28=180" [Linear pair]

22+b=180° [Linear pair]

23+2c=180" [Linear pair]

Add the above three equations, we get 21+za+z2+zb+23+2c=180° +180° + 180°

→ (21+ 22 +23) + 2a + 2b + zc=540"

→ 180°+ 2a + 2b + c = 540*

→ 2a + 2b +2c=540" - 180*=360" Thus sum of exterior angles of a triangle is 360⁰.

Answer 2

Answer:

Solution:-

Let the angles in ΔABC  ∠A= ∠1, ∠B= ∠2,and  ∠C= ∠3 and the exterior angles of A,B and C be  ∠a, ∠b and  ∠c respectively.

We know sum of all the angles in a triangle =180 degrees

= ∠1+ ∠2+ ∠3=180 degrees

From the figure,

 ∠1+ ∠a=180 degrees [Linear pair]

 ∠2+ ∠b=180 degrees [Linear pair]

 ∠3+ ∠c=180 degrees [Linear pair]

Adding the above equations,

= ∠1+ ∠a+ ∠2+ ∠b +∠3+ ∠c=180 degrees+180 degrees

=( ∠1+ ∠2+ ∠3)+ ∠a+ ∠b +∠c=540 degrees

=180 degrees + ∠a+ ∠b+ ∠c=540 degrees

= ∠a+ ∠b+ ∠c=540 degrees -180 degrees

= ∠a+ ∠b+ ∠c=360 degrees

Therefore, sum of exterior angles of a triangle =360 degrees

Hope it helps you.

Thank you