Question

in adjoining figure pq parallel to RS find x and y ​

Answer 1

/ RAC = / BAS -------( vertically opposite

angles )

but , ( / RAC = 65° )

:. / BAS = 65°

/ OAR + / OAB + / BAS = 180°

30° + / OAB + 65° = 180°

:. / OAB + 95° = 180°

:. / OAB = 180° - 95°

:. / OAB = 85°

/ RAB + / PBA = 180° ---------( interior

angles )

but, / RAB = / RAO + / OAB

= 30° + 85°

:. / RAB = 115°

and, / PBA = / PBO + / OBA

:. / PBA = 25° + y

/ RAB + / PBA = 180°

:. 115° + 25° + y = 180°

:. 140° + y = 180°

:. y = 180° - 140°

:. y = 40°

NOW ,

In triangle OAB ,

/ x + / y + / OAB = 180°

:. / x + 40° + 85° = 180°

:. / x + 125° = 180°

:. / x = 180° - 125°

:. x = 55°

:. y = 40° and

X = 55°