Question

If any two sides of a triangle are
produced beyond its base and the exterior
angles this obtained are bisected, then
these bisectors will include an angle equal to​

Answer 1

Step-by-step explanation:

Let the triangle be with angles a, b, c with base angles b and c.

The triangle formed by the given bisectors has the angles x, y and p.

P is the angle formed by the bisector.

Now 2x =a+c

Therefore x =

2

a

+

2

c

similarly y =

2

a

+

2

b

again P =180

∘

−(x+y)

substituting for x and y we get P =180

∘

−(

2

a

+

2

c

)−(

2

a

+

2

b

)

=a+b+c−

2

a

−

2

c

−

2

a

−

2

b

=

2

b

+

2

c

=

2

1

( sum of the base angles