In ΔUVW, U
W
‾
UW
is extended through point W to point X,
m
∠
U
V
W
=
(
3
x
+
16
)
∘
m∠UVW=(3x+16)
∘
,
m
∠
W
U
V
=
(
2
x
+
8
)
∘
m∠WUV=(2x+8)
∘
, and
m
∠
V
W
X
=
(
8
x
−
18
)
∘
m∠VWX=(8x−18)
∘
. Find
m
∠
W
U
V
.
m∠WUV.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

i you goofed up when writing this, because hnot is not a word minusf is not either. i cannot answer   because of that.

step-by-step explanation:

answer4 to the second power is 16

and 4 to the third power is 64,