+0

# ​ Using the diagram below, find x.

0
152
2 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
+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
+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 °   Feb 17, 2020