Maths-
General
Easy

Question

In triangle A B C comma 2 angle A equals 3 angle B equals 6 angle C then angleA =?

  1. 30°    
  2. 60°    
  3. 90°    
  4. 120°    

hintHint:

T h e space s u m space o f space a l l space a n g l e s space o f space t h e space t r i a n g l e s space i s space 180 degree. space C o m p a r e space angle A space w i t h space t h e space o t h e r space a n g l e s space a n d space s u b s t i t u t e space t h e m space i n space t h e space e q u a t i o n.

The correct answer is: 90°


    G i v e n comma
2 angle A space equals space 3 angle B thin space equals space 6 angle C

T o space F i n d comma
angle A

H e r e comma
2 angle A space equals space 3 angle B
therefore space angle B space equals space fraction numerator 2 angle A over denominator 3 end fraction space space space space space space space space space.... open parentheses 1 close parentheses

2 angle A space equals space 6 angle C
therefore space angle C space equals space space fraction numerator 2 angle A over denominator 6 end fraction space equals space space fraction numerator angle A over denominator 3 end fraction space space space space space space space space space space.... open parentheses 2 close parentheses

N o w comma space w e space k n o w space t h a t space s u m space o f space a l l space a n g l e s space o f space a space t r i a n g l e space i s space 180 degree
H e n c e comma
angle A space plus space angle B space plus space angle C space equals space 180 degree
F r o m space e q u a t i o n space open parentheses 1 close parentheses space a n d space open parentheses 2 close parentheses comma
angle A space plus space space fraction numerator 2 angle A over denominator 3 end fraction space plus space space fraction numerator angle A over denominator 3 end fraction space equals space 180 degree
space fraction numerator 3 angle A space plus thin space 2 angle A space plus space angle A over denominator 3 end fraction space equals space 180 degree
space fraction numerator 6 angle A over denominator 3 end fraction space space equals space 180 degree
2 angle A space space equals space 180 degree
angle A space equals space fraction numerator 180 degree over denominator 2 end fraction
therefore angle A space space equals space 90 degree

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