A picture frame is shaped as a heptagon. The measure of one angle is 126°. The remaining interior angles are congruent. What is the measure of each remaining interior angle in the picture frame?

180°

150°

129°

171°

Question

A picture frame is shaped as a heptagon. The measure of one angle is 126°. The remaining interior angles are congruent. What is the measure of each remaining interior angle in the picture frame? 

 180° 

 150° 

 129° 

 171°

zepp · Answer

First of all, can you find the sum of interior angles of a heptagon?

zepp · Answer

How many vertices there are in a heptagon?

anonymous · Answer

180degrees (n-2) so in your question n=7 and 

the sum is 180(7-2)=180*5= 900 degrees


but 900 isnt one of the answers

cwrw238 · Answer

heptagon has total angles = 7 * (180 -  (360/7)) =  900 degrees

zepp · Answer

Ok great!

zepp · Answer

Now you know that for any arbitrary heptagon, the sum of all interior angle is 900 degrees.

cwrw238 · Answer

(900 - 126) / 6 is the answer to your q

zepp · Answer

There you have one, one of the angles is 126 degrees and the rest are congruent

Can you build up an equation for that?

zepp · Answer

@cwrw238 I wanted her to find the answer ;(

anonymous · Answer

so it would be 129 right?

zepp · Answer

So yeah, sir cwrw238 showed the final step; here's how he proceeded:

Since the other 6 angles are congruent and the 7th angle is 126 degrees, let the one of the remaining angle be x

$6x + 126=900$ would be the equation you'll get.

zepp · Answer

Yes.

anonymous · Answer

yes thats what i did.

anonymous · Answer

Thanks for the help everyone :D (:

zepp · Answer

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