SOLUTION: the measure of angles of a regular pentagon , (x-5), (x-6), (2x-7) ,x and(2x-2). find the value of x?

Question 1031172: the measure of angles of a regular pentagon , (x-5), (x-6), (2x-7) ,x and(2x-2). find the value of x?
Found 2 solutions by Bakr.R, ikleyn:
Answer by Bakr.R(8) (Show Source): You can put this solution on YOUR website!
The question mentions the angles of a regular pentagon, with that information, we may assume that this polygon, or pentagon rather, has the properties of a regular polygon which means all sides are equal, and all angles are equal (meaning that they are the exact same).

The sides are irrelevant, being unknown they may be infinite, and the question does not require you to find them, so ignore that, and focus on the angles.

They give us five values, which are the values of the angles in the pentagon, and we know the sum interior angles (the total of the angles inside the shape), is equal to 540� (http://www.mathsisfun.com/geometry/interior-angles-polygons.html), and so, we can equal all the measurements in the question to 540. Let's start with a regular polygon:
. Now, let's fill out the information into the polygon:
Keep in mind, that it is NOT definite that x is equal to 108 since its an angle on its own, this diagram is just to make the method simpler, and the question did not state that each value belongs in each separate angle.
Now, we may deduce the equation:
, Let's simplify the equation.
Now, we are able to solve for x

And so, the answer is x=80�, and degrees is for using the right unit of measure, since x is in the measurement of angles, don't forget that, or the answer may be marked as incorrect, but hopefully it wouldn't cause much of a problem.
Good luck!
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.
the measure of angles of a regular pentagon , (x-5), (x-6), (2x-7) ,x and(2x-2). find the value of x?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

As it is formulated in the post, the problem has no solution (and does not make sense).

If you take off the word "regular" from the condition, then the problem HAS the solution, as explained by the other tutor.

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