Q. 144.8( 6 Votes )
In a ABC, ∠C = 3 ∠B = 2(∠ A + ∠ B). Find the measure of each one of ∠A, ∠B and ∠C.
Answer :
We know that the sum of angles of a triangle is 180°
i.e. ∠A + ∠B + ∠C = 180°
The given relation is ∠C = 3 ∠B = 2(∠A + ∠B) … (1)
⇒ 3 ∠B = 2(∠A + ∠B)
⇒ 3 ∠B = 2 ∠A + 2 ∠B
⇒ 2 ∠A = ∠B
⇒ ∠A = ∠B/2
Substituting values in terms of B in equation (1),
∠B/2 + ∠B + 3 ∠B = 180°
∠B/2 + 4 ∠B = 180°
∠B(9/2) = 180°
∠B = 180 × 9/2
∠B = 40°
Substituting B value in (1),
∠C = 3 ∠B = 3(40) = 120°
And ∠A = ∠B/2 = 40/2 = 20°
The measures are ∠A = 20°, ∠B = 40°, ∠C = 120°.
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