question_answer

In the adjoining figure \[\angle XOZ={{120}^{{}^\circ }}\]where O is the centre of the circle then \[\angle \mathbf{XYZ}\] is equal to

A)  \[{{110}^{{}^\circ }}\]                      

B)  \[{{120}^{{}^\circ }}\]   

C)  \[{{90}^{{}^\circ }}\]                                   

D)  \[{{40}^{{}^\circ }}\]

Correct Answer: B

Solution :

(b): Reflex angle \[XOZ={{360}^{{}^\circ }}-{{120}^{{}^\circ }}={{240}^{{}^\circ }}\] \[\therefore \]\[\angle XYZ\] = Angle at the circumference \[=\frac{240}{2}={{120}^{{}^\circ }}\]