Maths-
General
Easy

Question

In the figure, stack B C with bar on top parallel to stack D E with bar on top comma angle A C B equals 60 to the power of ring operator end exponent comma angle A E D equals 80 to the power of ring operator end exponent text  and  end text angle B A C equals 90 to the power of ring operator end exponent. text  Then  end text angle B A E equals ?

  1. 20°    
  2. 30°    
  3. 70°    
  4. 110°    

The correct answer is: 70°


    G i v e n space t h a t
angle A C B equals 60 to the power of ring operator comma angle A E D equals 80 to the power of ring operator space a n d space angle B A C equals 90 to the power of ring operator
L e t s space a s s u m e space A E space m e e t s space B C space a t space p o i n t space F
S i n c e space B C space i s space p a r a l l e l space t o space D E space a n d space A E space i s space a space t r a n s v e r s a l space
angle A F B thin space equals angle A E D space left parenthesis c o r r e s p o n d i n g space a n g l e s right parenthesis
angle A F B space equals space 80 to the power of ring operator to the power of blank
I n space t r i a n g l e space A F C
angle A F C plus angle A F B space equals space 180 to the power of ring operator space left parenthesis s u p p l e m e n t a r y space a n g l e s right parenthesis
angle A F C space equals 180 to the power of ring operator minus 80 to the power of ring operator
angle A F C space equals space 100 to the power of ring operator
angle A F C plus angle A C F plus angle F A C equals 180 space left parenthesis A n g l e space s u m space p r o p e r t y right parenthesis
100 to the power of ring operator plus 60 to the power of ring operator plus F A C equals 180 to the power of ring operator
angle F A C equals 20 to the power of ring operator
angle B A C equals angle B A E plus angle F A C
90 to the power of ring operator equals 20 to the power of ring operator plus angle B A E
angle B A E equals 70 to the power of ring operator

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