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.

Question

asked Nov 27, 2021 188k views

2 Answers

Martin Thurau · Answer 1 · 2021-12-01T11:21:37+0000

Answer:

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

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

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.