Question

prove that the exterior angles of Fidget spinner (Triangle) is 360°​

Answer 1

Answer:

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Answer 2

Draw the required figure.

Consider $\[\Delta \]ABC$ in which $\[\angle \]A = 1, [\angle \]B = 2 and [\angle \]C = 3$

Let the exterior angles of A, B and C be $\[\angle \]a, \angle \]b and \angle \]c$ respectively.

Know that sum of angles in a triangle is $180\[^ \circ \]$

Therefore,  $\[\angle \]1 + \angle \]2 + \angle \]3 = 180^ \circ \]$

Observe that from the figure,

$\[\angle 1 + \angle a = {180^ \circ }\]$  [Linear pair]-------(1)

$\[\angle 2 + \angle b = {180^ \circ }\]$  [Linear pair]--------(2)

$\[\angle 3 + \angle c = {180^ \circ }\]$ [Linear pair]---------(3)

Add equations (1), (2) , and (3).

$\[\angle 1 + \angle 2 + \angle 3 + \angle a + \angle b + \angle c = {180^ \circ }\] + {180^ \circ }\] + {180^ \circ }\]$

$\[\Rightarrow \]\angle 1 + \angle 2 + \angle 3 + \angle a + \angle b + \angle c = {540^ \circ }\]$

$\[\Rightarrow \]{180^ \circ }\] + \angle a + \angle b + \angle c = {540^ \circ }\]$

$\[\Rightarrow \]\angle a + \angle b + \angle c = {540^ \circ }\] - {180^ \circ }$

$\[\Rightarrow \angle a + \angle b + \angle c = {360^ \circ }\]$

Hence, the sum of exterior angles of a triangle is ${360^ \circ }$.