Question

Given: y ll z

Prove: m25+ m2 2 + m26 = 180°
L
A
M
1
2
3
y
4
5
6
7
Z
С
B
Assemble the proof by dragging ties to
the Statements and Reasons columns.

Answer 1

Answer: yes

Step-by-step explanation: yes

Answer 2

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`

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.