Question

one of the diagnols of a rhombus is equal to one of its side. Find the angles of the rhombus

Answer 1

Answer:

One of the diagonals of a rhombus is equal to its one side. Find all the angles of the rhombus.

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ANSWER

Diagonal of rhombus is equal to side of rhombus (given)

Diagonal divides the Rhombus into two equal parts so it forms an equilateral triangle

All the angle be 60

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and ∠BAC=∠ABC=∠BCA=60

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∠B=∠D=60

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Let ∠A and ∠C be x

∠B+∠D+∠A+∠C=360

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⇒60

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+60

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+x+x=360

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⇒2x=360−120

⇒2x=240

∴x=120

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∴∠A=120

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,∠B=60

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,∠C=120

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,∠D=120

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Answer 2

Question

1. One of the diagonals of a rhombus is equal to its sides. Find the angles of the rhombus.

Solution

Let ABCD be a rhombus such that it's diagonal BD is equal to its sides.

$\sf{i.e. \: AB=BC=CD=AD=BD} \\ \sf{=>∆ABD \: and \: ∆BCD \: are \: equilateral} \\ \sf{∆A = ∆C=60°} \\ \sf{∆A+∆B=180° =>60°+∆B=180°} \\ \sf{∆B=120°=∆D} \\ \sf{∆A=60°=∆C \: and∆B=∆D=120°}$

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