Question

find the value of angle ABD in the adjoining figure also find the value of angle ABC if angle c=3 angle ABC
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Answer 1

Answer:

Angle ABD = 30 degree

Angle ABC = 20 degree

Answer 2

Answer:

The complete question is,

In the figure given below find angle abd also find angle abc if angle c = 3 angle abc = 2 (angle a + angle b)

Given,

∠c = 3 ∠b = 2 (∠a + ∠b) ...(1)

Let, ∠ a = x

∠ b = y

⇒ ∠ c = 3 ∠b = 3y

from (1), let us consider first and last terms

∠c = 2 (∠a + ∠b)

⇒ 2∠a + 2∠b - ∠c = 0 ...(a)

as we know that, the sum of interior angles of a triangle is 180°, we have,

∠a + ∠b + ∠c = 180° ...(b)

solving equations (a) and (b), we get,

∠ c = 120°

∠c = 3 ∠b ⇒∠ b = ∠c/3 = 120°/3

∠ b = 40°

∠a + ∠b + ∠c = 180°  ⇒∠a + 40° + 120° = 180° ⇒∠a + 160° = 180° ⇒∠a = 180° - 160°

∠ a = 20°