1. Which of the following could be the angle measure of a triangle a) 55, 55, 90
b) 24, 48, 108 c) 23, 60, 83 d) 50, 57, 73

Step-by-step explanation:

In order for these to be the angle measures of a triangle, they have to add up to equal 180 degrees by the Triangle Angle-Sum Theorem.  For

a. 55 + 55 + 90 = 200 so a is not a triangle

b. 24 + 48 + 108 = 180 so b is a triangle

c. 23 + 60+ 83 = 166 so c is not a triangle

d. 50 + 57 + 73 = 180 so d is a triangle

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!

because its not ur topic and its not for is for homework not that.