question_answer

    In the following figure, ABC is an equilateral triangle and BDC is an isosceles right triangle, right angled   at   D,   then   the measurement of ?        

Answer:

    In the given figure,  is an equilateral triangle such that Now,                                              ...(i) [ angle opposite to equal sides are equal] Similarly,                               ...(ii) [ angle opposite to equal sides are equal] From Eqs. (i) and (ii), we get              ...(iii) Now,     [ sum of three angles of a triangle is 180°] From Eq. (iii), we get                 and  is an isosceles right triangle.                           [ angle opposite to equal sides are      equal] ...(iv) and                                     [given] Now, [sum of three angles of a triangle is 180°]