(02.06)in the figure below, lines m and n are parallel:

two parallel lines are shown crossed by a transversal. the angles are labeled with number 1-8. the angles on line m where the line is crossed by the transversal are 1, 2, 3, and 4 in clockwise order from top left. the angles on line n where the line is crossed by the transversal are 5, 6, 7, and 8 in clockwise order from top left.

in the diagram shown, ∠2 measures 77 degrees. what is the measure of ∠4?

5 degrees
77 degrees
103 degrees
180 degrees

"77 degrees"

Step-by-step explanation:

If you read the questions carefully, you will see that ∠2 and ∠4 are opposite angles to each other, or vertical angles.

We know that vertical angles are EQUAL to each other.

Hence,

∠4 = ∠2  [which is 77]

So, ∠4 = 77°

38.5

step-by-step explanation:

lets say, first number = r

second number = 3r+7

total = 49

(r)+(3r+7)= 49

4r+7 = 49

4r = 42

r = 42/4

r= 10.5

3r+7 = 3(10.5)+7 = 38.5

hope this

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