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Math Help - Complementary Angles?

  1. #1
    Member aldrincabrera's Avatar
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    Smile Complementary Angles?

    ,.,good day,.,
    ,.somethings been buggling my mind lately,.,.i have encountered this theorem on geometry,.,it says "If two angles are complementary, then both are acute"
    so i have this question "is zero degree the complement of 90 degrees???if so,.then both are not acute since acute angles are angles less than 90,.,please help me with this,.,.thnx
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  2. #2
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    Re: Complementary Angles?

    Quote Originally Posted by aldrincabrera View Post
    theorem on geometry,.,it says "If two angles are complementary, then both are acute" so i have this question "is zero degree the complement of 90 degrees???if
    In a course in axiomatic geometry, most authors use this definition:
    An angle is the union of two non-collinear rays with a common endpoint.
    So that rules out both a degenerate angle and a so-called ‘straight angle’.
    In fact, Jay Greenberg has the following theorem in his text:
    \left( {m\angle A} \right)^ \circ \text{ is a real number and }0<\left( {m\angle A} \right)^ \circ<180.

    So strictly speaking we would not have an angle of measure zero.
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  3. #3
    Member aldrincabrera's Avatar
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    Re: Complementary Angles?

    ,.,sir,.,i was proving the theorem and i ended up with this,.plss tell me if im doing it correctly,.
    here is my proof.,
    let alpha and beta be complementary angles,
    then alpha + beta = 90.
    we show that alpha < 90 and beta<90.
    Suppose alpha >equal to 90 or beta >equal to 90,
    then alpha+beta >equal to 90 in either cases.
    thus alpha<90 and beta <90,.

    am i wrong sir??thnx
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    Re: Complementary Angles?

    Quote Originally Posted by aldrincabrera View Post
    ,.,sir,.,i was proving the theorem and i ended up with this,.plss tell me if im doing it correctly,.
    here is my proof.,
    let alpha and beta be complementary angles,
    then alpha + beta = 90.
    we show that alpha < 90 and beta<90.
    Suppose alpha >equal to 90 or beta >equal to 90,
    then alpha+beta >equal to 90 in either cases.
    thus alpha<90 and beta <90,.
    If the sum of two positive numbers is 90 then each must be less than 90.
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  5. #5
    Member aldrincabrera's Avatar
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    Re: Complementary Angles?

    ,.but sir,.,am i on the right track??
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: Complementary Angles?

    Let \alpha and \beta be complementary angles so indeed:
    \alpha+\beta=90
    If you want to show: \alpha<90 and \beta<90.
    You have to do that for positive numbers!

    Because if you take \alpha=-240° and \beta=330
    Then \alpha+\beta=90 but \beta is not <90.

    So you have to assure you work with positive numbers.
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