In the figure, `POQ` is a line. The value of `x` is

Options

A. `20^(@)`
B. `25^(@)`
C. `30^(@)`
D. `35^(@)`

Answer

A

Explanation

Since, POQ is a line segment .
`:. " " /_POQ = 180^(@)`
`rArr " " /_POA + /_AOB + /_BOQ = 180^(@)`
`rArr " "40^(@) + 4x + 3x = 180^(@)`
[pitting `/_POA = 40^(@), /_AOB = 4x and /_BOQ = 3x`]
`rArr " " 7x = 180^(@) - 40^(@)`
`rArr " " 7x = 140^(@`
`rArr " " x = 140^(@) /7 `
`:. " " x = 20^(@)`