Question

When the three sides of a triangle are produced as
shown:

Show that x+y+z= 360°
( Hint x = <1 + <2, z = <1 + <3.
<y= <2 + <3. Adding their both sides we get the result. )




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Answer 1

Answer:

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Answer 2

Step-by-step explanation:

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

To prove: ∠DCA+∠FAE+∠FBD=180∘

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∘

So we get

∠DCA+∠FAE+∠FBD=2(180∘)

∠DCA+∠FAE+∠FBD=360∘

Therefore, it is proved.

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