Answer:
160
Explanation:
First you want to know the formula for the sum of the interior angles of polygons. If you look at those that are wasy, such as triangles and quadrilaterals and then even pentagons you could figure out, you'll be able to get it is (n-2)*180 where n is the number of sides. Then of course to find how much one angle is, as long as the shape is a REGULAR polygon, you divide that sum by however many angles there are. for instance we know a triangle has a sum of 180, and the formula proves it. Then divide 180/3 to find the measure of each angle so long as they are all equal in a regular triangle, or equilateral triangle. This gets us each angle is 60.
Now, you are given how much each angle is, so we can use this to find n.
140 = (n-2)180/n = 180 - 360/n Subtract 180 from both sides
-40 = -360/n Multiply both sides by -n
40n = 360 Finally divide both sides by 40
n = 9
So that means the first shape is a 9 sided regular polygon, or a nonagon.
The question then asks for the size of one interior angle of something with 2n sides, or in other words 2*9 or 18. So an 18 sided figure. Well let's use the formula again, just without knowing the answer.
(n-2)180/n
(18-2)180/18
2880/18
160
So the measure of each angle of an 18 sided regular polygon is 160 degrees.
Let me know if there was something you didn't understand.