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प्रश्न
In parallelogram FIST, find ∠SFT, ∠OST and ∠STO.
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उत्तर
Given, ∠FIS = 60°
Now, ∠FTS = ∠FIS = 60° ...[∵ Opposite angles of a parallelogram are equal]
Now, FT || IS and TI is a transversal,
Therefore, ∠FTO = ∠SIO = 25° ...[Alternate angle]
∴ ∠STO = ∠FTS – ∠FTO
= 60° – 25°
= 35°
Also, ∠FOT + ∠SOT = 180° ...[Linear pair]
⇒ 110° + ∠SOT = 180°
⇒ ∠SOT = 180° – 110° = 70°
In ΔTOS,
∠TSO + ∠OTS + ∠TOS = 180° ...[Angle sum property of triangle]
∴ ∠OST = 180° – (70° + 35°) = 75°
In ΔFOT,
∠FOT + ∠FTO + ∠OFT = 180°
⇒ ∠SFT = ∠OFT
= 180° – (∠FOT + ∠FTO)
= 180° – (110° + 25°)
= 45°
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