Question

For the rhombus below, find the measures of ∠1, ∠2, ∠3, and ∠4.

Answer 1

∠1 = 116 ° , ∠2 = 32° , ∠3 = 116 ° and ∠4 = 32°

Explanation:

∠2 = 32° (The diagonals of a rhombus bisect pairs of opposite angles)

Opposite sides of a rhombus are parallel ,so

∠2 = ∠4 (Alternate interior angles )

∠4 = 32°

32° + ∠4 + ∠3 = 180° (angle sum property of a triangle)

64° + ∠3 = 180°

∠3 = 180 - 64

∠3 = 116°

∠3 =∠1 (in a rhombus opposite angles are equal )

∠1 = 116°