The sum of the measures of the angles of a parallelogram is 360°. In the parallelogram on the right, angles A and D have the same measure as well as angles C and B. If the measure of angle C is eight timeseight times the measure of angle A, find the measure of each angle.

A = 20 degree

B = 160 degree

C = 160 degree

D = 20 degree

Step-by-step explanation:

If the measure of angle C is eight timeseight times the measure of angle A

That means C = 8A

But According to the question, angles A and D have the same measure as well as angles C and B.

That is, B = 8A and D = A

If A + B + C + D = 360

Let us substitute for B, C and D

A + 8A + 8A + A = 360

18A = 360

A = 360/18 = 20

Therefore

A = 20 degree

B = 8 × 20 = 160 degree

C = 8× 20 = 160 degree

D = 20 degree

The angles measure A = 20 degrees, B= 160 degrees, C = 160 degrees and D = 20 degrees.

Step-by-step explanation: One of the properties of a parallelogram is that opposite angles are equal. Hence we are given that angles A and D have the same measurement. Angles C and B also have the same measurement since they are also opposite each other. If angle C is eight times angle A, then angle C can be expressed as 8A, and the same applies to angle B. So, the four angles can be expressed as;

A + A + 8A + 8A = 360

(The sum of the four angles in a parallelogram equals 360 degrees)

2A + 16A = 360

18A = 360

Divide both sides of the equation by 18

A = 20

Therefore angle A = 20 and angle D = 20

Angle B = 160 and angle C = 160

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