Step-by-step explanation:
Let point O be any point in the triangle. Join line segments OD, OE and OF.
There are now 3 triangles inside the triangle DEF.
Let the sum of angles in each of these triangles be x.
It follows that 3x = Sum of angles at point O + Sum of angles in triangle DEF = 360° + x.
3x = 360° + x, 2x = 360°, x = 180°.
Hence the sum of angles in any triangle is 180°.
