PQR is the tangent at the point Q to a circle with centre O. AB is a chord of the circle parallel to the tangent, such that \(\angle BQR=50^\circ\). What is the measure of \(\angle AQB\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 80°
By the alternate segment theorem, the angle between the tangent QR and the chord QB equals the angle QB makes in the other segment, \(\angle QAB\). Since \(AB\parallel PR\), the transversal QB also makes equal alternate angles.
\(\angle QAB=\angle BQR=50^\circ\) (alternate segment)
\(\angle QBA=\angle BQR=50^\circ\) (alternate angles, \(AB\parallel PR\))
In \(\triangle AQB\): \(\angle AQB=180^\circ-50^\circ-50^\circ=80^\circ\)
