In Fig. 3, $PQ$ is a chord of a circle and $PT$ is tangent at $P$ such that $\angle QPT = 60°$, then the measure of $\angle PRQ$ is ________.

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In Fig. 3, $PQ$ is a chord of a circle and $PT$ is tangent at $P$ such that $\angle QPT = 60°$, then the measure of $\angle PRQ$ is ________.

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Accepted Answer

Step 1: $\angle QPT = 60°$ (angle between tangent and chord). By alternate segment theorem, $\angle QRP = 60°$ (angle in alternate segment). But $\angle PRQ$ is the angle in the major segment. $\angle PRQ = 180° - 60° = 120°$

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