Using the diagram below, find x.
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.
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