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# Vertical Angles and Linear Pairs Problem.

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Visualize the setup of vertical angles. Now, the angle measures allow for this problem to become more difficult. The measurements are 7y-92, y-3, 3x-1, and an unknown angle that is vertical to 3x-1. Are you able to figure out the values of x and y and explain your work? Thank you!

Edit: the y's and x's are opposite from each other...

Edit #2: Take this picture as an example, the measurements are not relative, but the bigger angles are the Y's and the smaller angles are the X's. Aug 20, 2018
edited by OwenT154  Aug 20, 2018
edited by OwenT154  Aug 20, 2018

### 4+0 Answers

#1
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Vertical angles are equal    soo   7y-92 = y-3       y= 14.833 degrees

All of the angles added should equal 360

7y-92  +  y-3   +  3x-1  + 3x-1  = 360

8y - 95   +  6x -2 = 360

8(14.833) - 95  + 6x  - 2 = 360

x = 56.38 degrees

Aug 20, 2018
edited by Guest  Aug 20, 2018
#2
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Assumig the "y"  angles are vertical ...we have that

7y - 92  = y  - 3       add 92 to both sides....subtract y from  both sides

6y   = 89

y  =  89/6  =   ( 14 + 5/6  )°

So....each  of these vertcal angles measures  (14 + 5/6  - 3)°   =  (11 + 5/6)°  = (71/6)°

So....the measure of each of the  other two vertical  angles  =    [ 360  - 2* (71/6) ] / 2 =

[ 360  -  (71/3) ] / 2  =     [ 1080 - 71 ] / 6  =  (168 + 1/6)°  =  (1009 / 6 )°

So...

3x - 1  = 1009/6

3x  =  1009/6 + 1

3x = 1009/6 + 6/6

3x  = 1015 / 6

x = (1015 / 18)°  = (56 + 7/18)°   Aug 20, 2018
#3
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Geometry is depressing... Anyways thank you!

OwenT154  Aug 20, 2018
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LOL!!!!!.....   CPhill  Aug 20, 2018