Three unrelated questions

I got #1, the answer is 86 degrees :)

1.  Let the largest angle   = a₅

Let the smallest angle   =  a₁

So

a₅ = a1  + 4d

a₅ - a₁  =  4d

But  a₅ - a₁  = 44

So  d  = 11

So the sum of the angles = 540

a₁ +( a₁+ d)  + (a₁ + 2d) + (a₁ + 3d) + (a₁ + 4d)   =  540

5a₁ + 10d  =  540

5a₁ + 10(11) = 540

5a₁  + 110   = 540

5a₁  = 430           divide both sides by 5

a₁  = 86°  =   the smallest angle

2.

Since ABE is equilateral....then angle ABE  = 60°

And since ABCD  is a square, then angle EBC =  90 - 60  = 30°

And since AC is a diagonal of the square, then  angle ACB  = 45°

Then, in triangle BPC,   angle BPC  must be   180  - 30 - 45  =  180  - 75  = 105°

3.

Let the side of the hexagon  = S

Then....the area  of the hexagon =  6(1/2)S^2*(√3/ 2)  = 3√3/2 S^2  units^2  

Now ...to determine the length of Fido's leash, L, we have

(1/2)S             L

_____   =      ______

sin (30)         sin (60)

(√3/2)S  =  L

So....the area  that Fido can cover is     pi  (√3/2S)^2  =  (3/4)pi*S^2 units^2

So  the fraction of the yard that Fido can cover is

(3/4)pi*S^2               (3/4)  pi                    6 pi               pi          √3

___________  =    ___________  =    ______  =    _____  =   ___  pi

3√3/2 S^2                  3√3/2                  12√3               2√3          6

So   a  = 3   and b  =  6     

And the product ab  is 6*3   =  18

EDIT TO CORRECT AN ERROR....!!!

Thanks so much CPhill, turn's out #3 was 18 but that might have been a glitch or a typo.