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In a ∆ABC, ∠ C = 3 ∠ B = 2 (∠A + ∠ B). Find the three angles. Q.5

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How i find the Angles of the given question. Because it is very important for board exams as well as competitive exams.  In a ∆ABC, ∠ C = 3 ∠ B = 2 (∠A + ∠ B). Find the three angles.

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  1. Given,

    ∠C = 3 ∠B = 2(∠B + ∠A)

    ∠B = 2 ∠A+2 ∠B

    ∠B=2 ∠A

    ∠A – ∠B= 0- – – – – – – – – – – –  (i)

    We know, the sum of all the interior angles of a triangle is 180O.

    Thus, ∠ A +∠B+ ∠C = 180O

    ∠A + ∠B +3 ∠B = 180O

    ∠A + 4 ∠B = 180O– – – – – – – – – – – – – – -(ii)

    Multiplying 4 to  equation (i) , we get

    8 ∠A – 4 ∠B = 0- – – – – – – – – – – – (iii)

    Adding equations (iii) and (ii) we get

    9 ∠A = 180O

    ∠A = 20O

    Using this in equation (ii), we get

    20O+ 4∠B = 180O

    ∠B = 40O

    3∠B =∠C

    ∠C = 3 x 40 = 120O

    Therefore, ∠A = 20O

    ∠B=40O

    ∠C = 120O

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