A picture frame is shaped as a heptagon. The measure of one angle is 216°. The remaining interior angles are congruent. What is the measure of each remaining interior angle in the picture frame?

186°

150°

114°

180°

Question

A picture frame is shaped as a heptagon. The measure of one angle is 216°. The remaining interior angles are congruent. What is the measure of each remaining interior angle in the picture frame?

186°

150°

114°

180°

anonymous · Answer

@dumbcow please help

anonymous · Answer

What is the sum of the interior angles of a dodecagon?

1800°

2160°

1620°

1440°

anonymous · Answer

@dumbcow @ParthKohli @UnkleRhaukus  someone help me, i mean thats what this website is for right :) yeahh thanks

anonymous · Answer

@ghazi

unklerhaukus · Answer

|dw:1357577804599:dw|

anonymous · Answer

ok so how do you know what to do, i'm lost

unklerhaukus · Answer

so you know a heptagon has seven sides right?

anonymous · Answer

yes

unklerhaukus · Answer

do you know a the angle sum of a triangle, 
what about a formula for the angle sum of a n- sided polygon,

anonymous · Answer

umm no i don't

unklerhaukus · Answer

well the sum of the internal angles in an n-sided polygon is $$(n-2)\times180°$$

a triangle has three sides so n=3 and the angle sum of a triangle is 180°

anonymous · Answer

so is that the answer then?

unklerhaukus · Answer

well can you find the internal angle sum , for a heptagon?

anonymous · Answer

no, i really don't remember all of this :/

unklerhaukus · Answer

well for the heptagon n=7

anonymous · Answer

oooook... well telling me that is cool but i mean if i just don't understand then it's not gonna make any sense to me but thanks for your help anyways i'll just guess the answer for this cause i seriously just don't get it.....ughhh

unklerhaukus · Answer

To find the sum of the internal angles in an heptagon use this formula with n=7

(n−2)×180°

unklerhaukus · Answer

if we now look at the picture we see that the internal angle sum is equal to 

6x+216°

unklerhaukus · Answer

set these results equal , and solve for x

anonymous · Answer

for x i got 36

unklerhaukus · Answer

are you sure?

anonymous · Answer

nope i mean i divide 216 by 6 thats what i think i should have done..

unklerhaukus · Answer

what did you get for 

(7−2)×180°=

anonymous · Answer

would that be 5 x 180 which would be 900

unklerhaukus · Answer

good , 

so now 

6x+216°=900°

anonymous · Answer

114

unklerhaukus · Answer

$$\color{red}\checkmark$$

anonymous · Answer

oh my gosh thank you :)

unklerhaukus · Answer

do you know how many sides a dodecahedron has ?

anonymous · Answer

no

anonymous · Answer

wait 10?

unklerhaukus · Answer

decahedron has ten,
do-decahedron has twelve

anonymous · Answer

What is the sum of the interior angles of a dodecagon? isn't this different from you  one you just ask about

unklerhaukus · Answer

now we know how many sides a dodecagon has and we have already learnt the formula for the internal angle sum , this second question is even easier

anonymous · Answer

well i'm not sure but i got 1800

unklerhaukus · Answer

correct

anonymous · Answer

oh ok lol thank you again :)

unklerhaukus · Answer

good work

anonymous · Answer

thank you