In the figure, `l" || "m and r" || "t`. They intersect at P, Q, R and S as shown in the figure. Find the angles of `angleSPQ and anglePSR`.

Answer

`125^(@),55^(@)`

Explanation

`angleP+angle Q=180^(@)` (since they are co-interior angles are `r" || "t`)
`rArr22x+15+9x+10=180^(@)`
`31x=180^(@)-25^(@)`
`31x=155^(@)`
`x=5^(@)`
`therefore angleP=22x+15^(@)`
`=22xx5^(@)+15^(@)`
`=110^(@)+15^(@)=125^(@)`
Given `l" || "m`,
`angleP+angleS=180^(@)`
`125^(@)+angleS=180^(@)`
`angleS=55^(@)`