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avatar+2448 

Please help >.<

 Feb 26, 2019
 #1
avatar+100516 
+3

First one....a little tricky

 

Note that both inscribed angles LMP and LNP   intercept the SAME arc LP  !!!

 

Therefore....their measues must be equal

 

So...this implies that

 

5x - 19 = 2x + 11    solve this RP

 

Then.....remember that arc LP     =  2  times ( measure of angle LNP)  = 2(2x + 11)

 

 

cool cool cool

 Feb 26, 2019
 #3
avatar+2448 
+1

Is it 62??

RainbowPanda  Feb 26, 2019
 #4
avatar+100516 
+2

x = 10

 

So

 

2 ( 2*10 + 11) =

 

2 (31) =

 

62  !!!!!   CORRECT !!!

 

 

cool coolcool

CPhill  Feb 26, 2019
 #5
avatar+2448 
+1

Thank you so much for your help!

RainbowPanda  Feb 26, 2019
 #2
avatar+100516 
+3

Second one

 

We have a cyclic quadrilateral

 

So remember that

 

R + P  = 180

 

12x - 27 + 4x - 1 = 180      simplify

 

16x - 28 = 180

 

16x = 208

 

x = 13

 

Now  R =  12(13) - 27   = 129°

 

And note that R   intercepts   arc QPS

 

So this arc measures 2 * angle R   =   2 * 129   =    258°

 

 

cool cool cool

 Feb 26, 2019

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