The angle ∠XZY is degrees, where P is the center of the given circle.
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Solution
Considering the arc minor ZY, ∠ZXY=12×∠ZPY ⇒∠ZXY=110o2=55o
Given, XQ is perpendicular to ZY, and it passes through the center. ∴Q is the midpoint, and ZQ = QY.
Also, QX is the common side of the △ZXQ and △YXQ.
Hence, △ZXQ≅△YXQ
(by SAS property)
∴ Corresponding angles must be equal, i.e., ∠ZXQ=∠YXQ=∠YXZ2 ⇒∠ZXQ=55o2=27.5o