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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.

RainbowPanda Mar 5, 2019

#1**+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°

CPhill Mar 5, 2019

#2**+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°

CPhill Mar 5, 2019