Question

The sum of all the exterior angles of a triangle is ___ (in degrees)​.

Answer 1

Let the exterior angles of the triangle be x, y and z respectively.

Then by exterior angle property, interior angles of the triangle will be $(180-x{)}^{\circ }$​, $(180-y{)}^{\circ }$​​, $(180-z{)}^{\circ }$​​

Using angle sum property of a triangle,

(180 - x) + (180 - y) + (180 - z) = 180

540 - (x + y + z) = 180

Therefore, x + y + z = ${360}^{\circ }$​