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avatar+2448 

Maybe this question will make sense??

I got 57 degrees for the first question but I don't know how to set up the second one. 

 Mar 5, 2019
 #1
avatar+100546 
+2

First one....this is known as the Intersecting Chord Theorem

 

In this case

 

measure of angle BCF = (1/2)( sum of arcs ED + BF)   .....so we have

 

(11x - 9)  = (1/2) [ ( 9x - 3) + (15x - 39) ]      multiply both sides by 2

 

2(11x - 9)  =  (9x - 3) + (15x - 39 )        simplify

 

22x - 18 =  24x - 42         add 42 to both sides, subtract 22x from both sides

 

24 = 2x 

 

12 = x

 

So.......arc  ED  =  9(12) - 3   =  105°

 

 

cool cool cool

 Mar 5, 2019
 #2
avatar+100546 
+2

Scond one....this is a little tricky !!!

 

Note that :

measure of angle WXZ +measure of angle  WXY = 180

(5x + 36) + WXY = 180

WXY = 180 - 5x - 36

WXY =  (144 - 5x)

 

And we can apply the Tangent Chord Theorem  that says that

 

2 * measure of angle WXY =  measure of  arc WX

And arc WX + arc WVX = 360

So we have 

 

2(144 - 5x) + (13x + 9)  = 360     simplify

 

288 - 10x + 13x + 9 = 360

 

297  + 3x = 360

 

3x = 63

 

x = 21

 

So....angle WXY =  ( 144 - 5(21) )   =  144 - 105  =  39°

 

 

cool cool cool

 Mar 5, 2019

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