Given /P O R=3x and /Q O R=2x+10^0dot If...

Given `/_P O R=3x` and `/_Q O R=2x+10^0dot` If `P O Q` is straight line, then the value of `x` is `30^0` (b) `34^0` (c) `36^0` (d) none of these

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Solution `/_POR` and `/_QOR` form a linear pair, therefore their sum must be supplementary.
That is;`/_POR + /_QOR = 180 ^@`
It is given that `BY = 3x`and `/_QOR = 2x + 10^@`
On substituting these two values above, we get:
`3x + 2x + 10^@ = 180^@`
`5x +10^@ = 180^@`
`5x = 180^@ -10 ^@`
`5x = 170^@`
`x =(170^@)/5`
`x = 34^@`
Hence option `(b) 34^0`.

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