Question

in the figure ,PQ is a tangent to a circle with Centre O. If angle OAB is equals to 30° find angle ABP and Angle AOB​

Answer 1

Answer:

angle ABP=60,angle AOB=120

Step-by-step explanation:

Answer 2

Since AO and OB is radius of circle

Therefore AO = OB

∠OAB = ∠OBA ( angle opp. to equal side)

∠OBA = 30°

NOW,

since radius is perpendicular to tangent

⇒∠ABO +ABP = ∠OBP

⇒ 30° + ∠ABP = 90°

∠ABP = 60°

And

In ΔAOB

∠OAB + ∠ABO + ∠AOB = 180° (ASP)

30 ° + 30 + ∠AOB = 180°

∠AOB = 120°

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