Question

The sides EF, FD and DE of a triangle DEF are produced in order forming three exterior angles
DFP, EDQ and FER respectively. Prove that ZDFP + ZEDO + ZFER = 360 ​

Answer 1

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Given :-

➤ The sides EF, FD and DE of a triangle DEF are produced in order forming three exterior angles  ∠DFP, ∠EDQ and ∠FER respectively.

To Prove :-

➤ ∠DFP + ∠EDQ+ ∠FER = 360°

Proof & Explanation :-

➤ For ∆ DEF, let the angles are x , y and z

then x + y + z = 180° ( Angle sum property of Triangle )

∠DFP = 180˚ − x         ....... (1)     [ Exterior angle theorem ]

∠EDQ = 180° − y         ....... (2)     [ Exterior angle theorem ]

∠FER = 180° − z          ....... (3)     [ Exterior angle theorem ]

Add these three equations, we get

∠DFP + ∠EDQ + ∠FER = 540° − (x + y + z)

                                                  = 540° − 180°

                                                  = 360°  

 

Hence, ∠DFP + ∠EDQ + ∠FER = 360°  

Hope It Helps You...