Question

A diagonal BD and the sides of the rhombus ABCD are of equal length.Find the measure of the angles of the rhombus

Answer 1

Given :- A diagonal BD and the sides of the rhombus ABCD are of equal length.Find the measure of the angles of the rhombus .

Solution :-

In ∆BDC, we have,

→ BD = BC (given)

and,

→ DC = BC (Sides of rhombus are equal.)

so,

→ BD = DC = BC

then, ∆BDC is a equaliteral ∆.

so,

→ ∠BCD = 60°

so,

→ ∠BAC = 60° (opposite angles of rhombus are equal.)

and,

→ ∠ABC = ADC = 180° - 60° = 120° (adjacent angles of rhombus are supplementary.)

Therefore, angles of rhombus :-

• ∠BCD = ∠BAC = 60°
• ∠ABC = ADC = 120° .

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