Please solve this and try not to leave links.
Dear Student,
Please find below the solution to the asked query:
We have our diagram , As :
Here we have join QT .
POT + TOQ = 180 , ( Linear pair angles ) Substitute value from given diagram and get
140 + TOQ = 180 ,
TOQ = 40 --- ( 1 )
And In TOQ , OT = OQ ( Radius ) so from base angle theorem we get
OQT = OTQ --- ( 2 )
And from angle sum property of triangle we get in TOQ :
OQT + OTQ + TOQ = 180 , Substitute values from equation 1 and 2 we get
OQT + OQT + 40 = 180 ,
2 OQT = 140 ,
OQT = 70
And OQT + RQT = 180 , ( Linear pair angles ) Substitute above value and get
70 + RQT = 180 ,
RQT = 110 ( Ans )
And PQT + PST = 180 , ( Opposite angles of cyclic quadrilateral PQTS ) Substitute value and get
70 + PST = 180 , ( As we show OQT = 70 and OQT = PQT same angles )
PST = 110, So
PSR = 110 --- ( 3 ) ( Same angles )
And from angle sum property of triangle we get in PSR :
PSR + SRP + RPS = 180 , Substitute values from equation 3 and given values we get
110 + SRP + 45 = 180 ,
SRP + 155 = 180 ,
SRP = 25
TRQ = 25 --- ( 4 ) ( Same angles )
And from angle sum property of triangle we get in RTQ :
RTQ + RQT + TRQ = 180 , Substitute values from equation 4 and as we solved , Then
RTQ + 110 + 25 = 180 ,
RTQ + 135 = 180 ,
RTQ = 45 ( Ans )
Hope this information will clear your doubts about topic.
For remaining queries we request you to post them in separate threads to have rapid assistance from our experts.
Regards
Please find below the solution to the asked query:
We have our diagram , As :
Here we have join QT .
POT + TOQ = 180 , ( Linear pair angles ) Substitute value from given diagram and get
140 + TOQ = 180 ,
TOQ = 40 --- ( 1 )
And In TOQ , OT = OQ ( Radius ) so from base angle theorem we get
OQT = OTQ --- ( 2 )
And from angle sum property of triangle we get in TOQ :
OQT + OTQ + TOQ = 180 , Substitute values from equation 1 and 2 we get
OQT + OQT + 40 = 180 ,
2 OQT = 140 ,
OQT = 70
And OQT + RQT = 180 , ( Linear pair angles ) Substitute above value and get
70 + RQT = 180 ,
RQT = 110 ( Ans )
And PQT + PST = 180 , ( Opposite angles of cyclic quadrilateral PQTS ) Substitute value and get
70 + PST = 180 , ( As we show OQT = 70 and OQT = PQT same angles )
PST = 110, So
PSR = 110 --- ( 3 ) ( Same angles )
And from angle sum property of triangle we get in PSR :
PSR + SRP + RPS = 180 , Substitute values from equation 3 and given values we get
110 + SRP + 45 = 180 ,
SRP + 155 = 180 ,
SRP = 25
TRQ = 25 --- ( 4 ) ( Same angles )
And from angle sum property of triangle we get in RTQ :
RTQ + RQT + TRQ = 180 , Substitute values from equation 4 and as we solved , Then
RTQ + 110 + 25 = 180 ,
RTQ + 135 = 180 ,
RTQ = 45 ( Ans )
Hope this information will clear your doubts about topic.
For remaining queries we request you to post them in separate threads to have rapid assistance from our experts.
Regards