Question

In Fig. 6.11, OP, OQ, OR and OS are four rays. Prove that `/_P O Q+/_Q O R+/_S O R+/_P O S=360o`

Answer 1

If we extend ray `QO` to T as shown in figure to point such that `QT` is a straight line, Then
`/_POQ +/_POT = 180^@->(1)`--> As, angle created by a straight line is always `180^@`
`/_SOT+/_SOQ = 180^@`
As, `/_SOQ = /_SOR+/_ROQ`
`/_SOT+/_SOR+/_ROQ = 180^@->(2)`
Adding (1) and(2),
`/_POQ +/_POT+/_SOT+/_SOR+/_ROQ = 360^@`
As,`/_POT+/_SOT = /_POS`,
`/_POQ +/_POS+/_SOR+/_ROQ = 360^@`