measure of angle NPQ

**rcs** · November 26th 2012, 06:25 AM

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

**Plato** · November 26th 2012, 07:02 AM

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.

**bjhopper** · November 26th 2012, 07:25 AM

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

**rcs** · November 26th 2012, 02:48 PM

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

**Plato** · November 26th 2012, 03:22 PM

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 $m(\angle NPM)$

**rcs** · November 26th 2012, 04:36 PM

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.

**Plato** · November 26th 2012, 05:50 PM

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.

**rcs** · November 27th 2012, 05:01 PM

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.

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