A person walked completely around the edge of a park beginning at the

VeritasKarishma

I have a doubt in the highlighted portion

If the park is a convex polygon, say a regular pentagon, wouldn't the turns be taken around vertex and so the degree of turn should be interior angle, and in case it is not convex as shown in the image attached by you, then for the obtuse angle we'll take exterior angle's measure. That's why we need to know if it is convex + the no. of sides

Kindly clarify!

This link shows you what exterior angles are. They are the same angles that are turned by the person.
https://www.mathsisfun.com/geometry/ext ... ygons.html

They are NOT the complete angles around the vertex.
Sum of exterior angles of a convex polygon are always 360. Think why.

VeritasKarishma

I understood why exterior angles will always add up to 360 because interior angles sum= (n-2)*180 degrees

My ques was why we are taking sum of exterior angles instead of interior angles. When a person makes a turn, the degrees he has turned should be the measure of interior angle Isn't it?

I don't know how to attach a picture in post, but hope you'll get what my doubt is

Thanks in advance!

(1) one of the turns is 80 degrees. this may not be a problem so much except we dont know how many sides there even are to this park, thus we dont know how many turns which are external angles of our polygon, or partial polygon NS

(2) we are told the park has 4 sides, all straight and each interior angle is less than 180 degrees. While this would seem NS since we dont have any individual angle measure, with geometry there is always that chance that variables can drop out in our calculation, so go ahead and try to set up a drawing. It needs to be four sides. also extend the sides so we have external angles on all sides. Label the internal angles x,y,z and the last one will be (360 - x - y -z) since any four sided object internal angles sum to 360. Now external angles form straight angles with their paired interior angle, so each exterior angle will be 180 minus our value. So our exterior angles are 180-x, 180-y, 180-z, and 180-(360-x-y-z). Sum these up and we get sum = 180 -x + 180 -y + 180-z +180 - 360 +x+y+z. so our variables drop out and we get 3(180) - 2(180) = 180 sufficient OA is B

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KarishmaB
Thank you for your helpful reply. To clarify, for both concave and convex polygons, the sum of the exterior angles are always 360?

Also "A person walked completely around the edge of a park beginning at the midpoint of one edge and making the minimum number of turns, each with the minimum number of degrees necessary" just is a fancy of way of asking for the exterior angles, correct? Tricky!

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