Find the < RQS

Dear Student,

The solution to you problem is as follows

Since PQ and PR are the tangent drawn from an external point to a circle, then

PQ = PR---------------------(1)

which means angle PQR = PRQ = 75⁰.

Also angle PQR = angle QSR---------------(Angles in alternate segment)

and angle PQR = angle SRQ----------------(Alternate interior angles since PQ parallel to SR.)

which means angle QSR = angle SRQ = angle PQR = 75⁰

so in triangle SQR, we have angle SQR + angle SRQ + angle QSR = 180⁰

Hence angle RQS = 30⁰

 

Regards

Team Topper's