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14 October, 19:23

The measure of one of the small angles of a right triangle is 45 less than twice the measure of the other small angle. Find the measure of both angles.

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  1. 14 October, 19:34
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    The other two small angles are 45° each

    Explanation:

    Given data in the problem:

    The triangle is a right triangle

    thus,

    one of the angle is 90°

    now,

    let the other two angles be x and y

    thus,

    it is given that:

    x = 2y - 45°

    also in a triangle

    sum of all the angles = 180°

    thus,

    x + y + 90° = 180°

    or

    x + y = 90°

    now, substituting the value of x from the above relation between x and y, we get

    2y - 45° + y = 90°

    or

    3y = 135°

    or

    y = 45°

    also,

    x = 2y - 45°

    or

    x = 2 * (45°) - 45°

    or

    x = 45°

    hence, the other two small angles are 45° each
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