3. Suppose that the interior angles of a convex hexagon are six numbers, each separated by a value of 1 degree from its neighbors. What
is the measure of the third largest angle?
degrees

The largest angle is A + 5 = 117.5 + 5 = 122.5 degree.  

Step-by-step explanation:

The sum of the interior angles of a regular hexagon is 720 degree.

Let the one angle is A.

So,

A + A + 1 + A + 2 + A + 3 + A + 4 + A + 5 = 720

6 A + 15 = 720

6 A = 705

A = 117.5

The largest angle is A + 5 = 117.5 + 5 = 122.5 degree.  

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!

answer: 80,000

step-by-step explanation:

the population doubles every day.

10,000*2=20,000 day 4

20,000*2=40,000 day 5

40,000*2=80,000 day 6