Question

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?

Answer 1

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

Answer 2

explain it further

Answer 3

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.

Answer 4

Do you understand it?

Answer 5

no

Answer 6

write down the second equation for me

Answer 7

i don't get it

Answer 8

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

Answer 9

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

Answer 10

60

Answer 11

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

Answer 12

then ?

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

how can we get the number of sides ?

Answer 17

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

Answer 18

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