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13 March, 06:20

Two angles are supplements if their sum is 180 degrees. The measure of one angle is seven-fifths the measure of its supplement. What is the measure of the smaller angle?

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  1. 13 March, 06:27
    0
    So the 2 angles are x and y

    'their sum is 180'

    x+y=180

    one is 7/5 of its supplement

    the supplement is the angle that, when added to it, equals 180 (x+y=180, x is the supplement of y and y is the supplement of x)

    let's say that the first one is x

    x is 7/5 of y

    'of' means multiply

    x=7/5 times y

    x=7y/5

    subsitute

    x+y=180

    subsitute 7y/5 for x

    7y/5+y=180

    convert y to 5y/5

    7y/5+5y/5=180

    add

    7y/5+5y/5 = (7y+5y) / 5=12y/5

    12y/5=180

    multiply both sides by 5

    12y=900

    divide both sides by 12

    y=75

    x+y=180

    x+75=180

    subtract 75 from both sides

    x=105

    the smaller angle is 75 degrees
  2. 13 March, 06:38
    0
    The measure of the smaller angle is 75 degrees.

    Given:

    Angle 1 + Angle 2 = 180 degrees

    Angle 1 = x

    Angle 2 = 7/5 * x

    x + 7/5 * x = 180

    x + 7x/5 = 180

    5 (x + 7x/5) = 5 (180)

    5x + 7x = 900

    12x = 900

    x = 900/12

    x = 75 degrees. Angle 1.

    Angle 2 = 7/5 * x = 7/5 * 75 = (7 * 75) / 5 = 525/5 = 105 degrees

    To check:

    Angle 1 + Angle 2 = 180 degrees

    75 deg + 105 deg = 180 deg

    180 deg = 180 deg
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