Question

The side EF,FD and DE of a triangle DEF are produced in order forming three exterior angles DFP,EDQ and FER respectively. Prove that

Answer 1

For triangle DEF, let the angles are x,y and z

then x+y+z=180

∠DFP=180 −x

∠EDQ=180 −y

∠FER=180 −z

Add these three equations, we get

∠DFP+∠EDQ+∠FER=540−(x+y+z)

=540-180 =360

Hence, ∠DFP+∠EDQ+∠FER=360