Question

50. In the given figure, PQ is the diameter of the
circle whose centre is O. Given ZROS = 42°,
calculate ZRTS.
R.
P
T
42°
S​

Answer 1

Answer:

Step-by-step explanation:

Join PS.

PQ is a diameter.

⇒  PSQ=90  

o

               [ Angle inscribe in a semicircle ]

⇒  ∠PSQ+∠PST=180  

o

      [ Linear pair ]

⇒  90  

o

+∠PST=180  

o

 

⇒  ∠PST=90  

o

 

∴   ∠SPT=  

2

1

​  

∠ROS

⇒  ∠SPT=  

2

1

​  

×42  

o

 

∴  ∠SPT=21  

o

 

In △PST,

⇒  ∠SPT+∠PTS+∠PST=180  

o

 

⇒  21  

o

+∠PTS+90  

o

=180  

o

 

⇒  ∠PTS=180  

o

−90  

o

−21  

o

 

⇒  ∠PTS=69  

o

 

∴  ∠PTS=∠RTS=69  

o