Question

if the sides of a triangle are produced in order, prove that the sum the exterior angles so formed is 360degree​

Answer 1

Answer:

Given: △ABC in which AB,BC and CA are produced to points D,E and F.

To prove: ∠DCA+∠FAE+∠FBD=180

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Proof :

From the figure we know that

∠DCA=∠A+∠B.(1)

∠FAE=∠B+∠C.(2)

∠FBD=∠A+∠C.(3)

By adding equation (1),(2) and (3) we get

∠DCA+∠FAE+∠FBD=∠A+∠B+∠B+∠C+∠A+∠C

So we get

∠DCA+∠FAE+∠FBD=2∠A+2∠B+2∠C

Now by taking out 2 as common

∠DCA+∠FAE+∠FBD=2(∠A+∠B+∠C)

We know that the sum of all the angles in a triangle is 180

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.

So we get

∠DCA+∠FAE+∠FBD=2(180

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)

∠DCA+∠FAE+∠FBD=360

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Therefore, it is proved.