Question

find the measures of the numbered angles in the rhombus, will give brainliest ! pls show how you solved it :)))

Answer 1

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°