1. all numbered streets runs parallel to each other. both 3rd and 4th streets are intersected by king ave. as shown:

(a) suppose a car is traveling west on 4th street and turns onto king avenue heading south. what is the measure of the angle created by the car's turning? explain your answer.

(b) suppose a car is traveling southwest on king avenue and turns right onto 3rd street. what is the measure of the angle created by the car's turning? explain your answer.

(c) suppose a car is traveling northeast on king avenue and turns right onto 4th street. what is the measure of the angle created by the car's turning? explain your answer

(a) 105°

(b) 75°

(c) 105°

Step-by-step explanation:

According to the options, we have,

(a) The car is travelling west on the 4th street and turns towards south on King Avenue.

So the angle (a) will be the angle made by the car's turning.

As, ∠(a) + 75° = 180°

i.e. ∠(a) = 180° - 75°

i.e. ∠(a) = 105°

(b) The car is travelling southwest on the King Avenue and turns right onto 3rd street.

So the angle (b) will be the angle made by the car's turning.

As, 3rd and 4th street are parallel. So, the corresponding angles have equal measures.

Thus, ∠(b) = 75°

(c) The car is travelling northeast on the King Avenue and turns right onto 4th street.

So the angle (c) will be the angle made by the car's turning.

As, ∠(c) + 75° = 180°

i.e. ∠(c) = 180° - 75°

i.e. ∠(c) = 105°

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!

where r the answers

step-by-step explanation: