SOLUTION: The interior angles of a certain traverse are given next. Determine whether each traverse closes (that is, forms a closed polygon). (HINT: You might begin by drawing each figure by

Algebra ->  Angles -> SOLUTION: The interior angles of a certain traverse are given next. Determine whether each traverse closes (that is, forms a closed polygon). (HINT: You might begin by drawing each figure by      Log On


   

Question 928081: The interior angles of a certain traverse are given next. Determine whether each traverse closes (that is, forms a closed polygon). (HINT: You might begin by drawing each figure by using a protractor.)
a. Angle A = 97.8°, Angle B = 61.3°, Angle C = 115.5, and Angle D = 82.6°
b. Angle A = 116°15’, Angle B = 89°45’ , Angle C = 103° 30’ Angle D = 128° 45’, and Angle E = 101° 45’
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
the measures of the angles of a polygon with n sides/angles add up to
%28n-2%29%2A180%5Eo .

a. ABCD could be a quadrilateral if A%2BB%2BC%2BD=%284-2%29%2A180%5Eo=2%2A180%5Eo=360%5Eo .
However, 97.8%5Eo%2B61.3%5Eo%2B115.5%5Eo%2B82.6%5Eo=357.2%5Eo so that traverse cannot close.

b. ABCDE could be a pentagon if A%2BB%2BC%2BD%2BE=%285-2%29%2A180%5Eo=3%2A180%5Eo=540%5Eo .
However, 116%5Eo%2B89%5Eo%2B103%5Eo%2B128%5Eo%2B101%5Eo=537%5Eo , and
%2215%27%22%2B%2245%27%22%2B%2230%27%22%2B%2245%27%22%2B%2245%27%22=%22180%27%22=2%5Eo , so
A%2BB%2BC%2BD%2BE=537%5Eo%2B2%5Eo=539%5Eo , and that traverse cannot close either.

NOTE: After those answers, the next question is why.
Why would someone make students add up so many ugly numbers, with so many chances of making mistakes? Why would someone give such a useless hint?
Anyone using common geometry tools would probably be 1%5Eo off.
Is this a problem given to firefighters in training, and any mistake could result in death, so they must learn to use the greatest care in their calculations and the highest precision protractors for their traverse drawing?