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If the angle between a tangent and the chord at the point of contact is 30°, the inscribed angle subtending the same chord on the arc on the other side of the chord measures:
A15 degrees
B150 degrees
C60 degrees
D30 degrees
Answer & Solution
Correct answer: D. 30 degrees
1. By the alternate segment theorem the tangent-chord angle equals the inscribed angle on the opposite arc.
2. The tangent-chord angle is 30°.
3. So the inscribed angle on the opposite arc is also 30°.
4. The inscribed angle on the same-side arc would be its supplement, 150°.
5. So the answer is 30°.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7 "Tangents" (pp 159-172, 2019 ed.)._
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