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avatar+1685 

 

Using the diagram below, find x.

  


A. 30


B. 32


C. 34


D. 28

 

 

 

In the figure below, CEF is an equilateral triangle.  Points B, C and E are collinear.  Points A, C and F are collinear; g = 40 degrees; and k = 55 degrees. Find j + k.

 

 

A. 80


B. 60


C. 65


D. 120

 Feb 17, 2020
 #1
avatar+179 
+2

For the first problem, we know that all the angles in a triangle add up to 180˚. That means: x + ( 2x + 5 ) + ( 3x + 7 ) = 180.

Since addition is associative, x + ( 2x + 5 ) + ( 3x + 7 ) = 180 is the same as x + 2x + 5 + 3x + 7 = 180.

Combining like terms, we get: 6x + 12 = 180.

After we move 12 to the other side so the x is iscolated, we get: 6x = 168.

Dividing each side by 6 gets us to: x = 28, so the answer to the first problem is D.

 

I hope this helped! I might've made a mistake, so if you catch one, please lmk! <3

 Feb 17, 2020
 #2
avatar+109740 
+3

Second problem

 

If  CEF is equilateral, then angle l    = 60 °

 

And agle C is supplementary  to this angle  = 120°

 

And angle  (j + k) is vertical to angle  C....so its measure  = 120 °

 

 

cool cool cool

 Feb 17, 2020

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