∠A = 80° and ∠ABC = 60°. BD and CD bisect angles B and C

• Geometry

In the figure given below, ∠A = 80° and ∠ABC = 60°. BD and CD bisect angles B and C respectively. What are the values of x and y respectively?

1. 10 and 130
2. 10 and 125
3. 20 and 130
4. 20 and 125

Answer

In triangle ABC,

∠A + ∠B + ∠C = 180°

∠C = 180° - 80° - 60° = 40°

x = 40°/2 = 20°

In triangle DBC,

x + y + 60°/2 = 180°

y = 180° - 20° - 30° = 130°

The correct option is C.