Question

PQRS is a rhombus $SRT={152}^{\circ }$ Find x,y and z.

Answer 1

In the given figure, the intersection of the diagonals is Y.
y= ${90}^{\circ }$ (Because the diagonals of a rhombus bisect each other at ${90}^{\circ }$)
$\angle$SRT = $\angle$QSR + y [external angle is equal to sum of opposite interior angle]
${152}^{\circ }$ = x + ${90}^{\circ }$
thus, x= ${62}^{\circ }$
In $\Delta$SPR, SP = SR
$\angle$SRP = $\angle$SPR = z
$\angle$SRP = ${180}^{\circ }$ - ${152}^{\circ }$ = ${28}^{\circ }$
Thus, z=${28}^{\circ }$