In the diagram below of triangle VWX, Y is a midpoint of VW and Z is a midpoint of W X. If mZY ZW = 64 - 2x, and mZVXZ= 92 - 92, what is the measure of ZV X Z?

m<VXZ = 56°

Step-by-step explanation:

Given that these lines are midpoints, they must be parrallel from each other which means that the corresponding angles are congruent.

Therefore the following equation is true:

m<YZW = m<VXZ

Since we now have this equation, substitute the expressions of the angles into the equation.

m<YZW = m<VXZ

| |

v v

92 - 9x = 64 - 2x

+9x +9x

92 = 7x + 64

-64 -64

28 = 7x

÷7 ÷7

4 = x

x = 4

Now since we know x is 4, substitute this back into the expressions given to find both of their measures.

x = 4 → 92 - 9x = 64 - 2x

92 - 9(4) = 64 - 2(4)

92 - 36 = 64 - 8

56 = 56 [these are the measures of both angles]

Therefore: m<VXZ = 56°

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

table 3 represents a direct variation function. : )