Question

p.q.r & S are parallel terms r - q =? please Explain me​

Answer 1

Answer:

$⇒  PQRS is trapezium. \\ </p><p></p><p>⇒   SP∥RQ           [ Given ] \\ </p><p></p><p>We \: know, \: sum \: of \: two \: angles \: between \: parallel \: lines \: is \: supplementary</p><p></p><p>$

$\pink{ \huge \cal ∴   ∠QRS+∠RSP={180 }^{ o  }}$

${\huge {\frak {\green{⇒  ∠QRS+{90 }^{ o}={180 }^{o}}}}}$

$\huge {\mathcal {\purple{⇒  ∠QRS={180 }^{ o}−{90 }^{ o}={90 }^{ o}}}}$

${\huge \bf⇒  ∠PQR+∠QRS+∠RSP+∠SPQ={360 }^{ o}}</p><p></p><p>$

$\huge \sf\purple{⇒  {100 }^{ o}+{90 }^{o}+{90 }^{ o}+∠SPQ={360 }^{ o}}</p><p></p><p>$

$\huge\red{ \bf ⇒  {280 }^{ o}+∠SPQ={360 }^{o}}</p><p></p><p>$

$\sf\orange{⇒  ∠SPQ={360 }^{ o}−{280 }^{ o}={80 }^{ o}}</p><p></p><p>$

$\color{cyan}∴   Measures \: \: \: \: of  \: \: \: ∠P  \: \: \: and \: \:  ∠R  \: \: \: are  \: \: {80 }^{o  }\: \: and  \: \: {90 }^{ o }$

Step-by-step explanation:

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