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Math Help - measure of angle NPQ

  1. #1
    rcs
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    measure of angle NPQ

    my attempt...since angle NRP is 138, and arc NMP = 138 x 2 is an intercepted arc.
    so then arc NRP is 360 - 276 = 84 degrees.

    how come in the book there is an answer that does not have solution ... then the answer is 112 degrees.


    Kindly help me on this..
    Thanks
    Attached Thumbnails Attached Thumbnails measure of angle NPQ-angle.jpg  
    Last edited by rcs; November 26th 2012 at 06:29 AM.
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    Re: measure of angle NPQ

    Quote Originally Posted by rcs View Post
    my attempt...since angle NRP is 138, and arc NMP = 138 x 2 is an intercepted arc.
    so then arc NRP is 360 - 276 = 84 degrees.
    how come in the book there is an answer that does not have solution ... then the answer is 112 degrees

    I get m\left( {\angle NPM} \right) = 68^ \circ  . That agrees with the answer in the textbook.
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    Re: measure of angle NPQ

    1 opposite angles of inscribed quadrilateral are supplementary
    2 angle NMP =180-138=42
    3 angle NPQ =180-42-70=68
    4 rcs should prove 1 as an exercise
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    Re: measure of angle NPQ

    Quote Originally Posted by Plato View Post
    I get m\left( {\angle NPM} \right) = 68^ \circ  . That agrees with the answer in the textbook.
    how did you get 68 degrees sir Plato? how is it possible... im sorry i cannot it.
    how come it agrees with the text book when the answer from the book is not 68 degrees

    kindly show it please.

    thanks
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    Re: measure of angle NPQ

    Quote Originally Posted by rcs View Post
    how did you get 68 degrees sir Plato? how is it possible... im sorry i cannot it.
    \begin{align*}m(\text{arc}(MP) &= 140\\ m(\text{arc}(PMN) &= 276\\\therefore~~ m(\text{arc}(MN) &=136\\ \\ \text{so}~~m(\angle NPM)&=68  \end{align*}.

    BTW the question asks for m(\angle NPQ) NOT m(\angle NPM)
    Last edited by Plato; November 26th 2012 at 03:26 PM.
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    Re: measure of angle NPQ

    Quote Originally Posted by Plato View Post
    \begin{align*}m(\text{arc}(MP) &= 140\\ m(\text{arc}(PMN) &= 276\\\therefore~~ m(\text{arc}(MN) &=136\\ \\ \text{so}~~m(\angle NPM)&=68  \end{align*}.

    BTW the question asks for m(\angle NPQ) NOT m(\angle NPM)


    thank you.. there is lacking in the solution that is why i was confused but your solution helped me a lot.

    Since arc MN is 136 so the angle NPM is 1/2 ( 136) = 68... the angle NPM and NPQ form linear pair, 180 - 68 = 112 for the measure of the angle NPQ.

    Thank you Sir Plato.
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    Re: measure of angle NPQ

    Quote Originally Posted by rcs View Post
    there is lacking in the solution that is why i was confused but your solution helped me a lot.

    Since arc MN is 136 so the angle NPM is 1/2 ( 136) = 68... the angle NPM and NPQ form linear pair, 180 - 68 = 112 for the measure of the angle NPQ.

    Surely you are not too lazy to complete the solution for yourself.
    I hope not. Otherwise, I have no attentions of helping you.
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    Re: measure of angle NPQ

    Quote Originally Posted by Plato View Post
    Surely you are not too lazy to complete the solution for yourself.
    I hope not. Otherwise, I have no attentions of helping you.

    hope also that when you help who would NOT cling Words an insulting statement!

    God Bless.
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