How are the angle measurements of the triangles related?

The two angles are similar!(*note I'm using the mathematical term similar)

Step-by-step explanation:

The reason is since the top angle is equivalent to 46 degrees that means the bottom two have to be the same and add up to 134 degrees.

On the bottom triangle the two degrees are 67 and 67 which add up to 134 degrees!

We also know all triangles add up to 180 degrees. So,

67 + 67 + x = 180.

134 + x = 180

Subtract 134 on both sides to get

x = 46 degrees! The same as the other top one! We can use and equation for the other triangle as well. :)

2x + 46 = 180

Subtract 46 to get

2x = 134

Divide by two to get

x = 67!

Hope this helped ya :)

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