The inscribed angle ∠XYZ for the given arc is 63°.
What is a measurement of angle in the circle?
"Take any circle with a center at the vertex of the angle θ. Then the radian measure of the angle is the ratio of the length of the subtended arc to the radius r of the circle".
For the given situation,
The diagram shows the angle of the arc = 126°
An inscribed angle is an angle with its vertex "on" the circle, formed by two intersecting chords.
Inscribed Angle = 1/2(Intercepted Arc)
∠XYZ = 1/2(∠XZ)
⇒ Inscribed Angle = [tex]\frac{1}{2} (126)[/tex]
⇒ Inscribed Angle = [tex]63[/tex]
Hence we can conclude that the inscribed angle ∠XYZ for the given arc is 63°.
Learn more about measuring angles of circles here
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