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:

The definition of a triangle is a polygon with three sides and three angles. A triangle's inside angles total 180 degrees, whereas its external angles total 360 degrees. Here we have given a figure and we have to find the angle a. Using the concept of equilateral triangle and diagonals, we will find angle x.

The correct answer is: 105°


    Here we have given a square ABCD. In that an equilateral triangle MDC is present.
    We will use the concept of an equilateral triangle and right angle triangle in this problem to solve. An equilateral triangle in geometry is a triangle with equally long sides. The three angles opposite the three equal sides are equal in size because the three sides are equal. As a result, with each angle measuring 60 degrees, it is sometimes referred to as an equiangular triangle.

    N o w space w e space h a v e space s q u a r e space A B C D comma space w h i c h space i m p l i e s colon
angle D C B equals 90 degree equals angle A B C
D B space b e i n g space t h e space d i a g o n a l comma space w e space g e t colon
angle D B C equals fraction numerator angle A B C over denominator 2 end fraction equals 45 degree
angle D B C equals angle C D B equals 45 degree
N o w space w e space h a v e space e q u i l a t e r a l space t r i a n g l e comma space s o colon
angle D M C equals space 60 degree equals angle M C D
angle N C B plus angle N C D equals angle D C B
angle N C B equals 90 degree minus 60 degree
angle N C B equals 30 degree
N o w space i n space t r i a n g l e space N C B comma space w e space h a v e colon
angle C N B plus angle N C B plus angle N B C equals 180 degree
P u t t i n g space t h e space v a l u e s space i n space i t comma space w e space g e t colon
angle x plus 30 degree plus 45 degree equals 180 degree
angle x equals 180 degree minus 75 degree
angle x equals 105 degree

    So here we were given a square PQRS and in that an equilateral triangle STR is present. We used the concept of equilateral triangle to solve the answer. So the angle x is equal to 105 degrees.

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