Question

In the given figure PQ||ST then find the value of X and y .​

Answer 1

Answer:

x = 65° and y = 50°

Step-by-step explanation:

∠TSO = 130°

∵ ∠SOQ = 130° (alternate interior angles are equal)

∴ ∠SOQ + ∠SOB = 180° (linear pair)

130° + ∠SOB = 180°

∠SOB = 180° - 130°

∠SOB = 50°

y = 50° (∠SOB is y)

_______

∠PQR + ∠OQR = 180° (linear pair)

115° + ∠OQR = 180°

∠OQR = 180° - 115°

∠OQR = 65° - - - - - 1

∠QOR = ∠SOB (vertically opposite angles are equal)

∠QOR = 50° - - - - - 2

∠OQR + ∠QOR + ∠ORQ = 180° (angle sum property of triangle)

Considering 1 and 2,

65° + 50° + ∠ORQ = 180°

115° + ∠ORQ = 180°

∠ORQ = 180° - 115°

∠ORQ = 65°

x = 65° (∠ORQ is x)