Question

In the figure below, $ABCD$ is a square, $MDC$ is an equilateral triangle. Find the value of $x$.

• A. $75^{\circ }$
• B. $90^{\circ }$
• C. $105^{\circ }$
• D. $60^{\circ }$

Answer 1

Answer: (C)

(i) The diagonal $BD$ bisects $\angle B$ and $\angle D$.
(ii) $BCD$ is an isosceles right-angled triangle. Using this find $\angle CBD$.
(iii) Given DMC is equilateral, so use this to find $\angle MCB$.
(iv) Sum of the angles of a triangle is $180^{\circ }$. Using this find $\angle x$.