question_answer

If the angle between a and c is\[25{}^\circ ,\]the angle between b and c is\[65{}^\circ ,\]and\[a+b=c,\]then the angle between a and b is

A) \[40{}^\circ \]                   

B)         \[115{}^\circ \]

C)  \[25{}^\circ \]                  

D)         \[65{}^\circ \]

E)  \[90{}^\circ \]

Correct Answer: E

Solution :

Let the angle between a and c is\[\theta \], then \[\theta =25{}^\circ \]and the angle between b and c is\[\alpha \], then\[\alpha =65{}^\circ \]. \[a+b=c\]                                            ...(i) So, by parallelograms property Resultant of a and\[b=a+b=c\][from Eq. (i)] So, angle between a and\[b=25{}^\circ +65{}^\circ =90{}^\circ \]