Question

In a rhombus PQRS, ∠SQR = 40° and PQ = 3 cm. Find ∠SPQ, ∠QSR and the perimeter of the rhombus.

Answer 1

PQRS is a Rhombus .

Join S, Q .

<SQR = 40° ( Given )

PQ = QR = RS = SP

i ) In ∆SQR ,

SR = RQ ,

<QSR = <SQR = 40°

[ Angles opposite to equal sides

are equal ]

and

<QRS + <QSR + <SQR = 180°

[ Angle sum property ]

=> <QRS + 40° + 40° = 180°

=> <QRS = 180° - 80° = 100°

<SPQ = <SRQ = 100°

[ Opposite angles are equal in a

Rhombus ]

Therefore ,

<SPQ = 100°

<QSR = 40°

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