Question

Find the missing angle measures in the given rhombus.

Answer 1

Explanation:

In rhombus, diagonals are perpendicular to each other.

∠2 = ∠3 = 90°

52° + ∠1 + ∠ 2 = 180° { Angle sum property of triangle}

52 + ∠1 + 90 = 180

∠1 + 142 = 180

∠1 = 180 - 142

∠1 = 38°

∠4 = ∠1 = 38° { Isosceles triangle}

Answer 2

1 = 4 = 38°, 2 = 3 = 90°

Explanation:

Because the diagonals of rhombi are perpendicular, ∠2 = ∠3 = 90°. Since the sum of angles in a triangle is 180°, ∠1 = 180° - 52° - 90° = 38°. If we look at the triangle with 1 and 4 as its base angles, we notice that it's an isosceles triangle, therefore ∠1 = ∠4 = 38°.