Question

PQ is a tangent at a point R of the circle with centre O. If angle TRQ=30°,find angle PRS.​

Answer 1

Answer:

Given ∠TRQ = 30°.

At point R, OR ⊥ RQ.

∠ORQ = 90°

⇒ ∠TRQ + ∠ORT = 90°

⇒ ∠ORT = 90° − 30° = 60°

ST is diameter, ∠SRT = 90° [∵ Angle in semicircle = 90°]

∠ORT + ∠ SRO = 90°

∠SRO + ∠PRS = 90°

∠PRS = 90° − 30° = 60°

Answer 2

Answer:

60°

Step-by-step explanation:

From figure,

Given that

∠TRQ=30

∘

∠TSR=∠TRQ=30

∘

(by Alternate segment therom).....(i)

∠TRS=90

∘

(Angle in semi circle)..............(ii)

From (i) & (ii) ∠RTS=60

∘

(Angle sum property in △SRT)

∴∠PRS=∠RTS=60

∘

(by Alternate segment therom)

hope it helps you

thanks

take care of yourself and your family

be at home be safe