Line ABC is a tangent to a circle at point B. If BP = BQ and \(\angle QBC = 72^\circ\), then find the value of \(\angle PBQ\):
36°
36° is correct.
By the alternate segment theorem, the angle between the tangent ABC and the chord BQ equals the angle that chord BQ subtends in the alternate segment, so \(\angle BPQ = \angle QBC = 72^\circ\).
Since BP = BQ, triangle BPQ is isosceles and the angles opposite the equal sides are equal: \(\angle BQP = \angle BPQ = 72^\circ\).
Angle sum in triangle BPQ: \(\angle PBQ = 180^\circ - 72^\circ - 72^\circ = 36^\circ\).
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