Question

In the figure, $BEST$ is a rhombus, Then the value of $y–x$ is

• A. $40°$
• B. $50°$
• C. $20°$
• D. $10°$

Answer 1

The correct option is A

$40°$

Explanation for the correct option:

Solve for the value of $y-x$

It is given that $BEST$ is a rhombus . So $TS\parallel BE$

$\Rightarrow \angle SBE=\angle BST=40°$ …[alternate angles between parallel lines are equal]

As diagonals of rhombus intersect at $90°$

$\therefore \angle y=90°$

Consider the triangle formed by the intersection of diagonals of the rhombus and vertices $S,T$

Also sum of opposite interior angles of a triangle is equal to the exterior angle

$$\begin{gathered} \Rightarrow x+\angle BST=y° \\ \Rightarrow x+40°=90° \\ \Rightarrow x=90°-40° \\ \Rightarrow x=50° \end{gathered}$$

$\therefore$ Value of $y-x=90°-50°=40°$

Hence option (A) is correct.