measure of angle NPQ

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November 26th 2012, 06:25 AM
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
November 26th 2012, 07:02 AM
Plato

Re: measure of angle NPQ

Quote:

Originally Posted by rcs

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.
November 26th 2012, 07:25 AM
bjhopper

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
November 26th 2012, 02:48 PM
rcs

Re: measure of angle NPQ

Quote:

Originally Posted by Plato

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
November 26th 2012, 03:22 PM
Plato

Re: measure of angle NPQ

Quote:

Originally Posted by rcs

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 $m(\angle NPM)$
November 26th 2012, 04:36 PM
rcs

Re: measure of angle NPQ

Quote:

Originally Posted by Plato

$\begin{align*}m(\text{arc}(MP) &= 140\\ m(\text{arc}(PMN) &= 276\\\therefore~~ m(\text{arc}(MN) &=136\\ \\ \text{so}~~m(\angle NPM)&=68 \end{align*}$ .

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.
November 26th 2012, 05:50 PM
Plato

Re: measure of angle NPQ

Quote:

Originally Posted by rcs

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.
November 27th 2012, 05:01 PM
rcs

Re: measure of angle NPQ

Quote:

Originally Posted by Plato

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.