PQRS is a rhombus in which the diagonal PR is produced to T.If angle SRT=152 degree,find x,y and z.

Please check my solution and do any rectifications if needed.
No links plz.

PQRS is a rhombus in which the diagonal PR is produced to T.If angle SRT=152 degree,find x,y and z. Please check my solution and do any rectifications if needed. No links plz. 0 9hombtU I sec AThßo) L TSO 15 1520

$$\begin{gathered} \mathrm{Your} \mathrm{solution} \mathrm{is} \mathrm{not} \mathrm{correct}. \angle \mathrm{TSO} \mathrm{is} \mathrm{not} \mathrm{any} \mathrm{angle}. \\ \mathrm{Kindly} \mathrm{find} \mathrm{the} \mathrm{solution} \mathrm{below}: \end{gathered}$$
Rhombus PQRS is given.

Diagonal PR is produced to T.

Also, .

We know that in a rhombus, the diagonals bisect each other at right angle.

Therefore,

Now,

In , by angle sum property of a triangle, we get:

Or, (Because O lies on SQ)

We have, .Thus the alternate interior opposite angles must be equal.

Therefore,

In ,we have

Since opposite sides of a rhombus are equal.

Therefore,

Also,

Angles opposite to equal sides are equal.

Thus,

But

Thus,

Hence the required values for x,y and z are , and respectively.