Answer:
As per the properties of parallel lines and interior alternate angles postulate, we can prove that:
[tex]m\angle 5+m\angle 2+m\angle 6=180^\circ[/tex]
Step-by-step explanation:
Given:
Line y || z
i.e. y is parallel to z.
To Prove:
[tex]m\angle 5+m\angle 2+m\angle 6=180^\circ[/tex]
Solution:
It is given that the lines y and z are parallel to each other.
[tex]m\angle 5, m\angle 1[/tex] are interior alternate angles because lines y and z are parallel and one line AC cuts them.
So, [tex]m\angle 5= m\angle 1[/tex] ..... (1)
Similarly,
[tex]m\angle 6, m\angle 3[/tex] are interior alternate angles because lines y and z are parallel and one line AB cuts them.
So, [tex]m\angle 6= m\angle 3[/tex] ...... (2)
Now, we know that the line y is a straight line and A is one point on it.
Sum of all the angles on one side of a line on a point is always equal to [tex]180^\circ[/tex].
i.e.
[tex]m\angle 1+m\angle 2+m\angle 3=180^\circ[/tex]
Using equations (1) and (2):
We can see that:
[tex]m\angle 5+m\angle 2+m\angle 6=180^\circ[/tex]
Hence proved.
