Answer:
AngleQSR= 27° (as angleQRS is 90° )
AnglePSR= 54°
AnglePQS= 180°-(63+27+27)
= 180°-127
= 53°
Take SQ as the diameter.
Angle SPQ = Half of Angle SOQ
(angle SOQ is 180° due to a line. So angle SPQ is half of angle SOQ = 90° )
So, Angle SPQ = 90°
In ∆ SPQ, Angle PQS = 180° - (27°+90°) = 63°
Now, (Angle PSQ + Angle RSQ) + (Angle PQS + Angle RQS) = 180°
( because PQRS is a cyclic quadrilateral and we know that sum of opp. sides in a cyclic quad. is = 180°)
So, Angle PSR = 180° - Angle PQR
= 180°-126° = 54°
Hence, Angle PQS = 63° and angle PSR = 54°.
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Answers & Comments
Answer:
AngleQSR= 27° (as angleQRS is 90° )
AnglePSR= 54°
AnglePQS= 180°-(63+27+27)
= 180°-127
= 53°
Verified answer
Take SQ as the diameter.
Angle SPQ = Half of Angle SOQ
(angle SOQ is 180° due to a line. So angle SPQ is half of angle SOQ = 90° )
So, Angle SPQ = 90°
In ∆ SPQ, Angle PQS = 180° - (27°+90°) = 63°
Now, (Angle PSQ + Angle RSQ) + (Angle PQS + Angle RQS) = 180°
( because PQRS is a cyclic quadrilateral and we know that sum of opp. sides in a cyclic quad. is = 180°)
So, Angle PSR = 180° - Angle PQR
= 180°-126° = 54°
Hence, Angle PQS = 63° and angle PSR = 54°.
I HOPE THIS ANSWER SHALL HELP YOU