in the given figure xy is a straight line op and oq stand on line xy
write all the pairs of adjacent angles and all the linear pairs of angles
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OP perpendicular XY
So, /_XOQ = /_QOY(each 90 degree)------------> (i)
/_QOP=/_XOQ- /_XOP --------------> (ii)
/_QOP = /_POY - /_QOY --------------> (iii)
But, /_QOP= /_ QOY - /_XOP[from (i)]
adding (ii) and (iii)
2/_QOP = /_QOY - /_XOP + /_POY - /_QOY
=> 2/_QOP = /_POY - /_XOP
So, /_XOQ = /_QOY(each 90 degree)------------> (i)
/_QOP=/_XOQ- /_XOP --------------> (ii)
/_QOP = /_POY - /_QOY --------------> (iii)
But, /_QOP= /_ QOY - /_XOP[from (i)]
adding (ii) and (iii)
2/_QOP = /_QOY - /_XOP + /_POY - /_QOY
=> 2/_QOP = /_POY - /_XOP
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