Question

in parallelogram fist find angle sft ,angle ost and angle sto​

Answer 1

$\huge\underline\blue {Answer}$

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Given:-

^SIO = 25°

^FIO = 35°

^FOT = 110°

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To find:-

^SFT, STO and ^OST

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Proof:-

In ∆OFT,

^OTF = ^OIS

^OTF = 25° (Interior alternate Angles)

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^OTF+^FOT+^OFT =180° ( Angle sum property )

25°+110°+^OFT = 180°

135°+^OFT = 180°

^OFT =180° - 135°

$\huge\fbox\green {OFT = 45°}$

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^STO = ^FIO ( Interior alternate Angles )

$\huge\fbox\pink {STO = 35°}$

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In ∆OST,

^FOT+^TOS =180° (Angles on straight line)

110°+^TOS = 180°

^TOS = 70°

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^TOS+^STO+^OST = 180° (Angle sum property)

70°+35°+^OST = 180°

^OST = 180°-110°

$\huge\fbox\purple {OST = 70°}$

Answer 2

Given:-

^SIO = 25°

^FIO = 35°

^FOT = 110°

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To find:-

^SFT, STO and ^OST

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Proof

In ∆OFT,

^OTF = ^OIS

^OTF = 25° (Interior alternate Angles)

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^OTF+^FOT+^OFT =180° ( Angle sum property )

25°+110°+^OFT = 180°

135°+^OFT = 180°

^OFT =180° - 135°

OFT=45°\huge\fbox\green {OFT = 45°}

OFT=45°

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^STO = ^FIO ( Interior alternate Angles )

STO=35°\huge\fbox\pink {STO = 35°}

STO=35°

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In ∆OST,

^FOT+^TOS =180° (Angles on straight line)

110°+^TOS = 180°

^TOS = 70°

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^TOS+^STO+^OST = 180° (Angle sum property)

70°+35°+^OST = 180°

^OST = 180°-110°

OST=70°\huge\fbox\purple {OST = 70°}

OST=70°