Question

In parallelogram FIST, find ∠SFT, ∠OST and ∠STO.

Answer 1

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°