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Mathematics 60 Online
OpenStudy (anonymous):

solve for the indicated quantity the measure of one interior angle of a regular polygon is sixty degrees more than twice the measure of an exterior angle at the same vertex.how many sides does this polygon have?

OpenStudy (anonymous):

\[Exterior \angle = \frac{360°}{n}\]\[Interior \angle = 180° - Exterior \angle\]\[Interior \angle=60^o\]

OpenStudy (anonymous):

explain it further

OpenStudy (anonymous):

n=number of sides. Plug in the known value of the interior angle into the second equation. Then solve for exterior angle. Then plug the exterior angle into the first equation and solve for n.

OpenStudy (anonymous):

Do you understand it?

OpenStudy (anonymous):

no

OpenStudy (anonymous):

write down the second equation for me

OpenStudy (anonymous):

i don't get it

OpenStudy (anonymous):

\[interior \angle=180^o-exterior \angle\] write that down in a piece of paper.

OpenStudy (anonymous):

can you tell me what the interior angle is equal to?

OpenStudy (anonymous):

60

OpenStudy (anonymous):

great lets rewrite the second equation the one you wrote down\[60^o=180^o -exterior \angle\] solve for the \[exterior \angle\]

OpenStudy (anonymous):

then ?

OpenStudy (anonymous):

can you do that first and tell me what you get? I already told you what to do after but I think you are not thinking things through one at a time so let's just focus on the exterior angle

OpenStudy (anonymous):

60=180-exterior< so transpose 180 to another side so the equation will be 60-180=-exterior< so this will become -120=-exterior < multiply by negative 1 the answer will be 120=exterior angle

OpenStudy (anonymous):

great plug that into this equation and solve for n \[exterior \angle=\frac{360^o}{n}\] n is the number of sides and your answer

OpenStudy (anonymous):

how can we get the number of sides ?

OpenStudy (anonymous):

n is the number of sides.....solve for n

OpenStudy (anonymous):

ah so the equation will be 120=360/n so cross multiply 120/1=360/n equals to 120n=360 divide both side by 120 so the answer is 3

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