Question

please solve it urgently with steps no direct answers please

Answer 1

Given, 3 ∠A = 4 ∠B = 6 ∠C

⇒ 3 ∠A = 4 ∠B    and    3 ∠ A = 6 ∠C

⇒ 3 / 4 ∠A = ∠B  and    3 / 6 ∠A = ∠C

⇒ 3 / 4 ∠A = ∠B  and    1 / 2 ∠A = ∠C

We know that the sum of all angles of the triangle is 180°. Therefore the sum of ∠A , ∠B and ∠C is 180°

⇒ ∠A + ∠B + ∠C = 180

⇒ ∠A + ( 3 / 4 ∠A ) + ( 1 / 2 ∠A ) = 180

⇒ $\dfrac{4\angle A +3 \angle A + 2 \angle A }{4}=180$

⇒ 9 ∠A = 180 x 4

⇒ ∠A = ( 180 x 4 ) / 9

⇒ ∠A = 20 x 4

⇒ ∠A = 80°

Therefore,

∠B = 3 / 4 ∠A = 3 / 4 x 80°

∠B =  3 x 20°

∠B = 60°

∠C = 1 / 2 ∠A = 1 / 2 x 80°

∠C = 1 x 40°

∠C = 40°

Therefore angles of the given triangle are 80°, 60° and 40° where ∠A = 80° , ∠B = 60° and ∠C = 40°

Answer 2

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