Question

In the figure, the circle is inscribed in a regular pentagon. P,Q and R are points of contact, find x.

Answer 1

Is this helpful?

Answer 2

why <RPQ=x?

Answer 3

Can you show that $$\Delta PQN\equiv\Delta RMQ$$

Answer 4

SAS

Answer 5

Yes
If so, RQ=PQ

Answer 6

yup

Answer 7

So $$\Delta RQP$$ is a isosceles triangle, Thus <RPQ=x

Answer 8

<RMQ=108
<MQR=180-108 / 2=36
<RQP=180-36*2=108
2x+108=180
x=36 ??

Answer 9

Yes. And the interesting fact is, this means PR\\MN.

Answer 10

really?

Answer 11

why, a=x implies???

Answer 12

ohh....i see...
angles in alt. segment....
thank you very much:)

Answer 13

you're welcome :)