Question 928081
the measures of the angles of a polygon with {{{n}}} sides/angles add up to
{{{(n-2)*180^o}}} .
 
a. ABCD could be a quadrilateral if {{{A+B+C+D=(4-2)*180^o=2*180^o=360^o}}} .
However, {{{97.8^o+61.3^o+115.5^o+82.6^o=357.2^o}}} so that traverse cannot close.
 
b. ABCDE could be a pentagon if {{{A+B+C+D+E=(5-2)*180^o=3*180^o=540^o}}} .
However, {{{116^o+89^o+103^o+128^o+101^o=537^o}}} , and
{{{"15'"+"45'"+"30'"+"45'"+"45'"="180'"=2^o}}} , so
{{{A+B+C+D+E=537^o+2^o=539^o}}} , 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^o}}} 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?