GREATLY APPRECIATE ANY HELP!!

A picture frame is shaped as a heptagon. The measure of one angle is 144 The remaining interior angles are congruent. What is the measure of each remaining interior angles in the picture frame?
a)126
b)180
c)174
d)150

Question

GREATLY APPRECIATE ANY HELP!!

A picture frame is shaped as a heptagon. The measure of one angle is 144 The remaining interior angles are congruent. What is the measure of each remaining interior angles in the picture frame?
a)126
b)180
c)174
d)150

directrix · Answer

How many sides does a heptagon have?

anonymous · Answer

Seven if i'm corrct

directrix · Answer

You are correct.
Now, we need to know the sum of the interior angles of the heptagon. 
Do you know the formula? It's okay if you don't; it's okay if you do.

anonymous · Answer

well the only formula i'm aware of is (n-2)x 180

directrix · Answer

That's it. So, where n is the number of sides, the sum of all the interior angles is
(7-2)*180 which is --> your turn to crank out the sum.

anonymous · Answer

900

anonymous · Answer

here is where im lost hehe xD

directrix · Answer

Great. So, we'll subtract that 144 angle from 900 and get 900- 144 = 756 degrees for the other six interior angles to share equally. That is because they are congruent and congruent angles have the same measure.

directrix · Answer

Any idea of what we should do to the 756 to get the measure of each of the remaining congruent angles. Your turn now.

anonymous · Answer

would i have to divide by the number of sides?

directrix · Answer

No. The number of sides gives the number of interior angles. 

But one of those seven interior angles had a measure of 144. We subtracted it from the total of all seven interior angles. Now, there are six angles left with a sum of 756. Remember that all six of those remaining angles have the same measure.

Does that make sense?

directrix · Answer

So, we'll divide 756 by what number? Your Turn

directrix · Answer

@RuthyCakes

anonymous · Answer

i got nothing , im sorry

directrix · Answer

No worries. 

Divide 756 by 6 and post what you get.

anonymous · Answer

126 is the outcome, but why is it specifically divided by 6?

anonymous · Answer

oh because there are 6 remaining right?

directrix · Answer

And, 126 is the answer to your question.

Checking it:

144 + 126*6 = 900 which is the sum of the interior angles of the septagon.

Yes, there are six congruent angles remaining after the 144 angle is subtracted.

anonymous · Answer

thank you so much ^_^ i appreciate your help a lot !!!

directrix · Answer

Glad to help. I like Geometry.