question_answer

\[\overrightarrow{\text{BA}}\bot \overleftrightarrow{\text{XY}}\] Which of the following statements are incorrect?

(i) \[\angle ABX+\angle ABY=180{}^\circ \]

(ii) \[\angle ABX=2\text{ right angles}\]

(iii) \[\angle \text{ABY=90 }\!\!{}^\circ\!\!\text{ }\]

(iv) \[\angle \text{XBY=90 }\!\!{}^\circ\!\!\text{ }\]

 

A) (i) and (ii) only  

B) (ii) and (iv) only  

C) (ii) and (iii) only

D) (i) and (iv) only

Correct Answer: B

Solution :

Since\[\overrightarrow{\text{BA}}\bot \overleftrightarrow{\text{XY}}\], \[\angle \text{ABX = 90 }\!\!{}^\circ\!\!\text{ }\]and \[\angle \text{ABY = 90 }\!\!{}^\circ\!\!\text{ }\] \[\therefore \angle ABX+\angle ABY=180{}^\circ \] is true. \[\angle ABX=90{}^\circ \Rightarrow \angle ABX=2\] right angles is false. \[\angle ABY\text{ }=\text{ }90{}^\circ \] is true. \[\angle XBY\text{ }=\text{ }90{}^\circ \] is false since \[\angle XBY=\text{ }\angle XBA+\text{ }\angle ABY\text{ }=180{}^\circ .\]