Question

Given: y ll z

Answer 1

Answer:

As per the properties of parallel lines and interior alternate angles postulate, we can prove that:

$m\angle 5+m\angle 2+m\angle 6=180^\circ$

Step-by-step explanation:

Given:

Line y || z

i.e. y is parallel to z.

To Prove:

$m\angle 5+m\angle 2+m\angle 6=180^\circ$

Solution:

It is given that the lines y and z are parallel to each other.

$m\angle 5, m\angle 1$ are interior alternate angles because lines y and z are parallel and one line AC cuts them.

So, $m\angle 5= m\angle 1$ ..... (1)

Similarly,

$m\angle 6, m\angle 3$ are interior alternate angles because lines y and z are parallel and one line AB cuts them.

So, $m\angle 6= m\angle 3$ ...... (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 $180^\circ$.

i.e.

$m\angle 1+m\angle 2+m\angle 3=180^\circ$

Using equations (1) and (2):

We can see that:

$m\angle 5+m\angle 2+m\angle 6=180^\circ$

Hence proved.

Answer 2

Answer:

Step-by-step explanation: