# Thread: measure of angle NPQ

1. ## 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

2. ## Re: measure of angle NPQ

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.

3. ## 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

4. ## Re: measure of angle NPQ

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

thanks

5. ## Re: measure of angle NPQ

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 $m(\angle NPM)$

6. ## Re: measure of angle NPQ

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.

7. ## Re: measure of angle NPQ

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.

8. ## Re: measure of angle NPQ

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.