+0  
 
+1
123
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avatar+64 

Find the measure of angels 1, 4, & 5  

https://uk.answers.yahoo.com/question/index?qid=20180514000823AA94xik

ps: Forget the ones that are circled that are number! 

THEMAN31  Jun 7, 2018
 #1
avatar+92997 
+2

Since arc SN  =  60°, the  angle 8  = 1/2 of this  = 30°

 

And arcs  SN, SQ, QP  and PN  sum  to 360°....so

 

SN   + SQ   + QP + PN

(60)  + ( x)  + (x + 40)  + (2x  - 16)  = 360      simplify

84  + 4x  = 360    subtract 84 from both sides

4x  = 276       divide both sides  by 4

x = 69°

 

So... arc QP  = x + 40  =  69 + 40  =  109

And angle 7  is 1/2 of this  = 54.5°

 

So  angle  6  = [ 180  - angle 8 - angle  7  ]  =   [ 180 - 30  - 54.5  ]  = 95.5°   

And since angle 5  is vertical to angle 6, its measure is also  95.5°

 

 

And angle  4 is supplemental to angle 6  so its measure is  180 - 95.5   = 84.5°

 

And angle 1  will have 1/2 the measure  of  the sum  of arcs SN and SQ =

 

(1/2)(60 + 69)   =

(1/2)(129)  =

64.5°

 

 

cool cool cool

CPhill  Jun 7, 2018
 #2
avatar+64 
+2

Thanks 

THEMAN31  Jun 7, 2018

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