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9 December, 00:22

In a triangle, Angle B is twice as large as Angle A. Angle C is five more than Angle B. What are the angle measurements of Angles A, B, and C?

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  1. 9 December, 00:40
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    The angle measurements of the Angles A, B, and C are 35°, 70° and 75° respectively.

    Step-by-step explanation:

    Sum of all angles in a triangle is = 180°

    Therefore, A + B + C = 180° ... (1)

    From the question, the statement shows that;

    B = 2A = => A = B/2 ... (2)

    C = 5 + B ... (3)

    Substitute for A and C in equation (1)

    (B/2) + B + (5+B) = 180°

    B/2 + B + 5 + B = 180°

    B/2 + 2B + 5 = 180°

    Multiply through by 2

    B + 4B + 10 = 360°

    5B + 10 = 360°

    5B = 360 - 10

    5B = 350

    B = 70°

    Since B is 70°, substitute for B in both equation (2) and (3) to get A and C respectively.

    A = B/2 = => 70/2 = 35°

    C = 5 + B = => 5 + 70 = 75°

    To proof A + B + C = 180°

    35° + 70° + 75° = 180°

    180° = 180°
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