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°
