Question

Question 41
In the figure, BEST is a rhombus, then the value of y - x is
a) ${40}^{\circ }$
b) ${50}^{\circ }$
c) ${20}^{\circ }$
d) ${10}^{\circ }$

Answer 1

Given: BEST is a rhombus, so,
$TS\parallel BE$
and BS is a transversal.
$\therefore \angle SBE=\angle TSB={40}^{\circ }$ [alternate interior anges]
$Also,\angle y={90}^{\circ }$ [diagonals of a rhombus bisect at ${90}^{\circ }$]

In $\Delta TSO$,
$\angle STO+\angle TSO+\angle SOT={180}^{\circ }$ [Angle sum property of a triangle]
$x+{40}^{\circ }+{90}^{\circ }={180}^{\circ }\Rightarrow x={180}^{\circ }-{90}^{\circ }-{40}^{\circ }={50}^{\circ }$
$\therefore y-x={90}^{\circ }-{50}^{\circ }={40}^{\circ }$