Find the value of x! justify your answer!

Use the Triangle exterior angle theorem. The definition of this theorem, is that the exterior angle you are solving for is the sum of the two opposite interior angles. Set the equation:

80 + x = 3x - 22

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract x and add 22 to both sides.

80 (+22) + x (-x) = 3x (-x) - 22 (+22)

80 + 22 = 3x - x

Simplify.

102 = 2x

Isolate the variable, x. Divide 2 from both sides.

(102)/2 = (2x)/2

x = 102/2

x = 51

Check. Plug in 51 to the equation given.

80 + x = 3x - 22

80 + (51) = 3(51) - 22

131 = 153 - 22

131 = 131 (True).

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18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.