Find the values of a and b from the adjoining figure.

Options

A. `a=38^(@)and b=35^(@)`
B. `a=37^(@)and b=36^(@)`
C. `a=37^(@)and b=35^(@)`
D. `a=40^(@)and b=35^(@)`

Answer

C

Explanation

Hence, OT stands on the straight line PQ, so
`anglePOT+angleQOT=180^(@)`
`rArr3a+22^(@)+47^(@)=180^(@)" (LPA)`
`rArr3a=180^(@)-22^(@)-47^(@)=111^(@)`
`rarr a=37^(@)" ".....(1)`
Also, `anglePOR+angleROS+angleSOQ=180^(@)" "(LPA)`
`rArr90^(@)+a+(b+180^(@))=180^(@)`
`rArr90^(@)+37^(@)+b+18^(@)=180^(@)" "` [ from (1)]
`:. b=180^(@)-145^(@)=35^(@)`
Hence, `a=37^(@)and b=35^(@)`