Question

If XY bisect angle MXN = 72⁰, then value of angle MXY will be what? please tell​

Answer 1

Answer:

ANSWER

Let the equations

y=m

1

x=0 and y=m

2

z are two straight lines represented by the given pair of straight line equations.

m

1

=tanα and m

2

=tanβ and β>α

Hence,

(y−m

1

)(y−m

2

)=y

2

=

b

2h

xy+

b

a

x

2

so,

m

1

−m

2

=

a

2b

and m

1

m

2

=

b

a

If θ be the angle subtended by angle bisector (y=mx) of the pair of straight line with the positive direction of x-axis, then m=tanθ

Now it is obvious that

θ−α=β−θ

So,

α+β=2θ

⇒tan(α+β)=tan(2θ)

⇒

1−tanαtanβ

tanα+tanβ

=

1−tan

2

θ

2tanθ

⇒

1−m

1

.m

2

m

1

+m

2

=

1−m

2

2m

⇒

1−a/b

2h/b

=

1−m

2

2m

⇒

b−a

h

=

1−m

2

2m

⇒h(1−m

2

)=(b−a)m

⇒h(1−m

2

)−(b−a)m=0.

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