Question

Which reason justifies Statement 5?

Answer 1

Answer:

Reason given in explanation

Step-by-step explanation:

1. Given : Lines A and B are parallel, C and D are transversals .

2. We know that if two lines are parallel then alternate interior angles are equal.

As lines A and B are parallel, $\angle Y=\angle 4$ ( $\angle Y , \angle 4$ are alternate interior angles )

3.  We know that if two lines are parallel then alternate interior angles are equal.

As lines A and B are parallel, $\angle Z=\angle 6$ ( $\angle Z , \angle 6$ are alternate interior angles )

4. As $\angle X\,,\,\angle 4\,,\,\angle 6$ lie on a straight line, $\angle X+\angle 4+\angle 6=180^{\circ}$

5. From point 2, 3, 4, we get

$\angle X+\angle 4+\angle 6=180^{\circ}\\\angle X+\angle Y+\angle Z=180^{\circ}$

Answer 2

Here, from the diagram it is clear that a triangle XYZ is formed as the lines b,c and D intersect.

Also, wkt,

Sum of three angles of a triangle is always 180°

The above is the justification for statement 5