Question

If in a rhombus, one side 5cm and one angle is 60°. Find the measure of other sides and angles.​

Answer 1

AB = BC = CD = AD = 5 cm

∠A = ∠C = 60°

∠B = ∠D = 120°

In a rhombus,

⇒ One side of rhombus = 5 cm

⇒ One angle = 60 degrees

We know that,

⇒ Rhombus: It is that quadrilateral in which all sides are equal.

⇒ All rhombus is a parallelogram.

Therefore, pair of opposite angles are equal.

Let,

A rhombus ABCD

⇒ Angle A = Angle C = 60 degrees

⇒ Angle B = Angle D = x

∠A + ∠B + ∠C + ∠D = 360°

By using property of sum angles of quadrilateral,

Substitute the values

= 60 + x + 60 + x = 360

= 2x + 120 = 360

= 2x = 360 - 120

= 2x = 240

= x = 120

⇒ ∠B + ∠D = 120°

Therefore,

All sides of rhombus are equal.

⇒ AB = BC = CD = AD = 5 cm

⇒ ∠B + ∠D = 120°

⇒ ∠A + ∠C = 60°