Question

One of the diagonals and one side of a rhombus are of equal length. Find the angles of the rhombus.

Answer 1

• ABCD is a rhombus.

⇒BD = BC ........(1)(given)

BC = CD .....(2)(side of rhombus)

From equations (1) and (2)

BD = BC = CD

⇒△BCD is equilateral triangle. (1 mark)

So, ∠BCD = 60°

• ∠C = ∠A = 60° (Opposite angles)

• ∠ABC = ∠ADC = 180 – 60 = 120° (Adjacent angles are supplementary).

• Angles of the rhombus are;

∠A = 60°, ∠ B = 120°, ∠C = 60°, and ∠D = 120° (1 mark)