In `DeltaPQR` and `DeltaMST`, `angleP=55^(@),angleQ=25^(@),angleM=100^(@)and angleS=25^(@)`. Is `DeltaQPR~DeltaTSM`? Why ?

Explanation

False
we know that, the sum of three angles of the triangles is `180^(@)`
In `DeltaPQR,angleP+angleQ+angleR=180^(@)`
`rArr55^(@)+25^(@)+angleR=180^(@)`
`rArrangleR=180^(@)-(55^(@)+25^(@))=180^(@)-80^(@)=100^(@)`
In `DeltaTSM angleT+angleS+angleM=180^(@)`
`rArrangleT+25^(@)+100^(@)=180^(@)`
`rArrangleT=180^(@)-(25^(@)+100^(@))`
`=180^(@)-125^(@)=55^(@)`

In `DeltaPQR and DeltaTSM`
`angleP=angleT,angleQ=angleS`
and `angleR=angleM`
`therefore DeltaPQR~DeltaTSM` [Since, all corresponding angles are equal]
hence, `DeltaQPR` is not similar to `DeltaTSM` , since correct correspondence is `harr`T,`QharrS` and `RharrM`.