Question

Please find me the value of x​

Answer 1

x = 60°

Explanation:

∠ ABO and ∠ CBO are a linear pair and sum to 180° , that is

∠ ABO + ∠ CBO = 180°

150° + ∠ CBO = 180° ( subtract 150° from both sides )

∠ CBO = 30°

∠ XYO and ∠ CBO are alternate angles and are congruent , so

∠ XYO = 30°

∠ XOY and ∠ COY are a linear pair and sum to 180° , then

∠ XOY + ∠ COY = 180°

∠ XOY + 90° = 180° ( subtract 90° from both sides )

∠ XOY = 90°

the sum of the 3 angles in Δ XOY = 180° , that is

x + 90° + 30° = 180°

x + 120° = 180° ( subtract 120° from both sides )

x = 60°

Answer 2

x = 60°

Explanation:

See picture below. When two parallel lines are cut by a transversal there are some special relationships.