Question

In an isosceles triangle, one of the equal angles measures ${50}^{\circ }$. The sum of all the exterior angles of the same 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 = ${360}^{\circ }$

If you count one exterior angle at each vertex, the sum of the measures of the exterior angles of any polygon is always 360°.