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10 March, 15:49

Angles x, y, and z are angles. if x and y are complementary angles, x and z are supplementary angles, and y and z add up to 190, what is the value of z - x - y, in degrees?

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  1. 10 March, 16:12
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    If x and y are complimentary ... x + y = 90

    if x and z are supplementary ... x + z = 180

    and y + z = 190

    x + y = 90 ... x = 90 - y

    x + z = 180

    90 - y + z = 180

    z = 180 - 90 + y

    z = 90 + y

    y + z = 190

    y + 90 + y = 190

    2y + 90 = 190

    2y = 190 - 90

    2y = 100

    y = 100/2

    y = 50 <===

    x = 90 - y

    x = 90 - 50

    x = 40 <===

    z = 90 + y

    z = 90 + 50

    z = 140 <===

    z - x - y = 140 - 40 - 50 = 50 <==
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