In the given figure, PQ is tangent to the circle with Centre at O, at the point B. If ∠AOB = 100° then ∠ABP, is equal to

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CBSE 10th Class Mathematics
Past year question paper
Year 2020
SET 1, Code Number – 30/2/1
Question Number – 7
construction geometry [line and circle]
opposite angle

Given that

∠ AOB = 100°

Since OA = OB

So ∠ OAB = ∠ OBA = 40°

Since PQ is tangent on the circle. So OB is perpendicular to PQ.

So,

∠ OBP = 90°

∠ OBA + ∠ ABP = 90°

∠ ABP = 90 – ∠ OBA

∴ ∠ ABP = 90° – 40°

∴ ∠ ABP = 50°