Q. 254.8( 6 Votes )

In Fig. 7, tangen

Answer :

PR = PQ (Tangents drawn from an external point are equal)

PQR = PRQ (Angles opposite to equal sides)


In ΔPQR,


PQR + PRQ + RPQ = 180° (Sum of all angles of a triangle is 180°)


PRQ + PRQ + 30° = 180°


2PRQ = 150°



Given that, RS||PQ


So, SRQ = PQR = 75° (Alternate interior angle)


Join OR and OQ.


ORP = 90° (tangent is perpendicular to the radius)


ORQ + QRP = 90°


ORQ + 75° = 90°


ORQ = 15°


In ΔORQ,


OQR = ORQ = 15° (Angles opposite to equal sides as OR = OQ = radius)


OQR + ORQ + ROQ = 180° (Sum of all angles of a triangle is 180°)


15° + 15° + ROQ = 180°


ROQ = 150°


Now, RSQ = ROQ/2 (Angle in the major sector)



In Δ RSQ,


RSQ + SRQ + RQS = 180° (Sum of all angles of a triangle is 180°)


75° + 75° + RQS = 180°


RQS = 30°


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