Question

If O is the centre of the circle.Find angle RTQ and RQT.

Answer 1

Angle POT +Angle TOQ=180
Angle TOQ=40
OT=OQ (radii)
Angle OTQ=Angle OQT
Consider triangle TOQ
By angle sum property, Angle TOQ+AngleOTQ+Angle OQT=180.
2Angle OTQ=140
OTQ=OQT=70
Angle OQT+Angle RQT=180
Therefore,Angle RQT=110
Consider cyclic quadrilateral PQTS
Angle P+Angle T=180
Angle T=135
Angle STQ+Angle RTQ=180
Therefore,Angle RTQ=45

Answer 2

Answer:

Step-by-step explanation:

Angle POT +Angle TOQ=180

Angle TOQ=40

OT=OQ (radii)

Angle OTQ=Angle OQT

Consider triangle TOQ

By angle sum property, Angle TOQ+AngleOTQ+Angle OQT=180.

2Angle OTQ=140

OTQ=OQT=70

Angle OQT+Angle RQT=180

Therefore,Angle RQT=110

Consider cyclic quadrilateral PQTS

Angle P+Angle T=180

Angle T=135

Angle STQ+Angle RTQ=180

Therefore,Angle RTQ=45