Question

In the given figure, `angleQPR=50^(@), angleQRS=135^(@)` and PQ = PR and ST = SR. Find the angle of `angleS.`

Answer 1

Correct Answer - `40^(@)`
In the figure, PQR and TRS are triangles.
In `DeltaPQR, PQ=PR`
`rArr angleQ=angleR`
`angleP+angleQ+angleR=180^(@)`
`50^(@)+angleR+angleR=180^(@)`
`2angleR=130^(@)`
`angleR=65^(@)`
`therefore angleQ=angleR=65^(@)`

In `DeltaTRS, angleTRS=135^(@)-65^(@)`
`angleTRS=70^(@)`
In `DeltaTRS, TS= SR`
`rArr angleSTR=angleTRS=70^(@)`
`rArr angleS=180^(@)-(70^(@)+70^(@))`
`angleS=40^(@)`