Maths-
General
Easy

Question

In the figure, stack B C with bar on top is extended both sides upto D, E. angle B A C equals ?

  1. 10°    
  2. 80°    
  3. 100°    
  4. none of these    

The correct answer is: 80°



    angle A B C plus angle A C B plus angle B A C space equals 180 to the power of ring operator space space space space left parenthesis a n g l e space s u m space p r o p e r t y space o f space t r i a n g l e right parenthesis space space space space space space space space space space space left parenthesis i right parenthesis space
space angle A B C plus angle B A C space equals 125 to the power of ring operator space space space space space space space space space space space space left parenthesis e x t e r i o r space a n g l e space i s space e q u a l space t o space s u m space o f space t w o space o p p o s i t e space i n t e r i o r space a n g l e s right parenthesis space space space space space space space space space space space space space space left parenthesis i i right parenthesis
space space angle B A C space plus angle A C B space equals 135 to the power of ring operator space space space space space space space space space space left parenthesis e x t e r i o r space a n g l e space i s space e q u a l space t o space s u m space o f space t w o space o p p o s i t e space i n t e r i o r space a n g l e s right parenthesis space space space space space space space space space space space space space left parenthesis i i i right parenthesis

space space 125 plus angle A C B equals 180 to the power of ring operator space space space f r o m space left parenthesis i right parenthesis
angle A C B space equals 180 minus 125 to the power of ring operator
space space space space space space space space space space space equals 55 to the power of ring operator
A l s o
55 to the power of ring operator plus angle B A C equals 135 to the power of ring operator space space space space space space f r o m space left parenthesis i i i right parenthesis
angle B A C equals 80 to the power of ring operator

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