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26 August, 01:22

The second angle of a triangle is 3 times as large as the first. The third angle is 50° more than the first. Find the measure of the smallest angle

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  1. 26 August, 04:26
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    Your smallest angle is 26°

    Angles in a triangle add up to 180°. This means:

    Angle1 + Angle2 + Angle3 = 180°

    The second angle of a triangle is 3 times as large as the first.

    Angle2 = 3 * Angle1

    The third angle is 50° more than the first.

    Angle3 = Angle1 + 50°

    Substitute these into the first formula, in terms of Angle1.

    Angle1 + (3 * Angle1) + (Angle1 + 50°) = 180°

    Expand and simplify.

    5 * Angle1 + 50° = 180°

    Put it into the formula Ax = B. You will have all the variables on one side and the integers on the other.

    5 * Angle1 + 50° = 180°

    5 * Angle1 + 50° - 50° = 180° - 50°

    5 * Angle1 = 130°

    Put it into the formula x = b. Solve to find 1 of the variable.

    5 * Angle1 = 130°

    5 * Angle1 / 5 = 130° / 5

    Angle1 = 26°

    Check this is right by substituting into the given formulas.

    Angle2 = 3 * Angle1

    Angle2 = 3 * 26

    78 = 3 * 26

    Angle3 = Angle1 + 50°

    Angle3 = 26 + 50°

    76 = 26 + 50°

    Angle1 + Angle2 + Angle3 = 180°

    26 + 78 + 76 = 180°
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