Question

In the following figure, if ABC and BDC are two
triangles, then x + y + z equals
C​

Answer 1

Answer:

x + y + z = 150°

Step-by-step explanation:

In ΔAOB

∵ ∠BOC is the external angle to the ΔAOB

∴ ∠BOC = ∠BAO +  ∠ABO

⇒ 95° = 60° + x

⇒ x = 35°

Similarly in ΔOCD

∠OCD + 30° = 95°

⇒ ∠OCD = 95° - 30°

               = 65°

∵ BCE is a straight line

∴ ∠OCD + y + z = 180°

⇒ y + z = 180° - 65°

            = 115°

Thus, x + y + z = 35° + 115°

                        = 150°

Hope this helps.