25. In Fig. 14.53, PQ is the diameter of the circle whose centre is O. Given angleROS = 42°. Calculate angleRTS
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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
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