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anonymous
 one year ago
#17 If the vertex angle of a regular polygon has measure 168 degrees, how many sides does it have?
anonymous
 one year ago
#17 If the vertex angle of a regular polygon has measure 168 degrees, how many sides does it have?

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mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1There is a formula that relates the number of sides of a polygon to the sum of the measures of the interior angles.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1\(S = (n  2)180\) where S = sum of the measures of the interior angles n = number of isdes of the polygon

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0let me try to solve real quick.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1What do you know about the sides and angles of a regular polygon?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0they're congruent right?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Yes. All angles are congruent.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1If all angles are congruent, and you know the sum of the measures of the angles, if you divide the sum by the number of angles, you get the measure of each angle, right?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Here is an example. Think of a square. A square is a regular polygon with 4 sides. The sum of the measures of the interior angles of a square is: \(S = (n  2)180 = (4  2)180 = 2(180) = 360\) Now we divide 360 by the number of angles, 360/4 = 90 That means each angle of a square measures 90 degrees. That makes sense because we know a square has 4 right angles.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now think of your problem. The unknown in your problem is the number of sides, n. The sum of the measures of the angles is \((n  2)180\) If we divide that sum by the number of angles, we get the measure of each angle: \(each~angle~measure = \dfrac{(n  2)180}{n} \)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1\( \dfrac{(n  2)180}{n} = 168\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1We first multiply both sides by n. Now think of your problem. The unknown in your problem is the number of sides, n. The sum of the measures of the angles is \((n  2)180\) If we divide that sum by the number of angles, we get the measure of each angle: \((n  2)180 = 168n \)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1We rewrite the left side: \(180(n  2) = 168n\) We distribute the 180 on the left side: \(180n  360 = 168n\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now we subtract 168n from both sides: \(12n  360 = 0\) We add 360 to both sides: \(12n = 360\) Divide both sides by 12: \(n = 30\) The polygon has 30 sides.
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