Question

149. In parallelogram FIST, find SFT, OST and ST0​

Answer 1

Answer:

∠SFT = 45°

∠OST = 75°

∠STO = 35°

Explanation:

In this parallelogram FIST,

FT ║SI

So, with TI as transversal, we can say that,

∠TIS =∠ITF [Alternate Interior Angles]

Similarly,

∠TIF =∠ITS [Alternate Interior Angles]

Now from figure,

∠ITS =∠OTS = ∠STO and ∠ITF = ∠OTF

So, ∠STO = 35°

From figure,

∠FOT = 110°

Then by linear pair concept,

∠FOT + ∠TOS = 180°

=> ∠TOS = 180° - 110° = 70°

Now, in Δ SOT,

∠STO = 35°

∠TOS = 70°

Then, ∠OST = 180° - [35° + 70°] = 75°

In Δ FOT,

∠OTF = 25°

∠FOT = 110°

Then, ∠OFT = 180° - (110° + 25°) = 45°

From figure,

∠OFT = ∠SFT

So,

∠SFT = 45°

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Answer 2

Step-by-step explanation:

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