Answer:
∠1 = 72°
∠2 = 54°
∠3 = 54°
∠4 = 72°
Step-by-step explanation:
In the isosceles triangle in which ∠4 is the top vertex angle and ∠3 & 54° are it's base angles. As it is an isosceles triangle , ∠3 = 54°
Using angle sum property of a triangle ,
∠4 + ∠3 + 54° = 180°
⇒ ∠4 + 54°+ 54° = 180°
⇒ ∠4 = 180° - 108° = 72°
Diagonals of a rhombus bisect the vertex angles of a rhombus. So,
∠2 = ∠3 = 54°
Also , opposite vertex angles of a rhombus are equal, So , ∠1 = ∠4 = 72°
As i said before put the center instead of (h,k) in the general formula and put r=1
so (x-(-2))^2 + (y-(-5)^2 = 1
(x+2)^2 + (y+5)^2 = 1
We have
The rational root theorem suggests that other possible roots may be -6, 6, -3, 3, -2, 2, -1, and 1. It turns out that 
is a root, since 
, so 
is also a factor and we have
Finally, we can factorize the remaining quotient easily:
so the other factors are , 
, and 
.
