Maths-
General
Easy

Question

If ABCD is a square, MDC is an Equilateral Triangle ,find the value of x .

  1. 75°    
  2. 90°    
  3. 105°    
  4. 60°    

hintHint:

diagonal bisects interior angles in square

The correct answer is: 105°


    I n space t r a i n g l e space M D C space
angle M C D equals space 60 degree space left parenthesis E q u i l a t e r a l space t r i a n g l e right parenthesis
sin c e space D B space i s space d i a g o n a l space o f space s q u a r e space A B C D
t h e r e f o r e space angle N D C equals 45 degree space left parenthesis d i a g o n a l space b i s e c t s space i n t e r i o r space a n g l e right parenthesis

n o w space i n space triangle N D C space
angle N D C plus angle D C N plus angle C N D space equals 180 degree left parenthesis A n g l e space s u m space p r o p e r t y space o f space a space t r i a n g l e space right parenthesis
45 degree space plus space 60 degree space plus angle C N D space equals 180 degree
angle C N D equals 75 degree

angle D N C space plus space angle C N B space equals 180 degree space left parenthesis s t a r i g h t space l i n e right parenthesis
75 degree plus x equals 180 degree
x equals 105 degree

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