@musiclover10045, i have been stuck in it for 1.5 hours, you

AC and CD are congruent, because C is the midpoint of AD. , this also means

BC and CE are congruent, because C is the midpoint of BE.  

Angles ACB and DCE are vertical angles which mean they are also congruent.  

Using the Side-Angle- Side theorem, Triangles ABC and DEC are congruent.

This means AB and DE are congruent, because corresponding sides of congruent triangles are congruent.

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!

the answer is b. 60. each interior angle in 120, so the exterior angle must be 60 in order to add up to 180

step-by-step explanation: