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 angleDFP + angleEDQ + angleFER = 360°.

Answer 1

1+2+3=180 where 1,2,3 are interior angle
now replace 1,2,3 by (180-DFP)+(180-EDQ)+(180-FER)=180 NOW u will get DFP+EDQ+FER=360

Answer 2

Answer:

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

then x+y+z=180

o

∠DFP=180

o

−x

∠EDQ=180

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−y

∠FER=180

o

−z

Add these three equations, we get

∠DFP+∠EDQ+∠FER=540

o

−(x+y+z)

=540

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−180

o

=360

o

Hence, ∠DFP+∠EDQ+∠FER=360

o