Question

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 $

Answer 1

Answer: (E)

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 $