1.

In the figure below, `2angleP=angleQOR`. OQ and OR are bisectors of `angleQ and angleR` respectively. Find `angleP`. A. `60^(@)`B. `70^(@)`C. `40^(@)`D. `80^(@)`

Answer» Correct Answer - A
`2 angleP=angleQOR`
In `DeltaPQR, angleP+angleQ+angleR=180^(@)" "`.(1)
`implies angleQ+ angleR=180^(@)-angleP`
In `DeltaOQR, angleOQR+ angleQOR+ angleORQ=180^(@)`.
`implies (angleQ)/(2)+2 angleP+(angleR)/(2)=180^(@)" "` (2).
`implies 2angleP+(180^(@)-angleP)/(2)=180^(@)`
`angleP=60^(@)`
Hence, the correct option is (a).


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