What is the missing reason in the proof

The correct option is 1.

Step-by-step explanation:

Given information: x║y, w is transversal line.

From the given figure it is clear that

                     (Definition of vertically opposite angles)

                     (Definition of corresponding angles)

According to the transitive property of congruent angles, if ∠1 ≅ ∠2 and ∠2 ≅ ∠3, then ∠1 ≅ ∠3.

Using transitive property of congruent angles, we get

The missing reason is transitive property, therefore the correct option is 1.

1760 kilometers

step-by-step explanation:

multiply the amount of time the plane took to travel by it's speed

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12